OPINION

RIPPLE, Circuit Judge.

A grand jury indicted William Mitchell, Jr., for his involvement in a long-running scheme to bribe the auditor of Cuyahoga County, Ohio, into awarding overvalued contracts for appraisal work to a company formed by Mr. Mitchell's law partners. The indictment included three counts: (1) conspiracy to commit bribery concerning programs receiving federal funds, in violation of 18 U.S.C. § 371; (2) bribery concerning programs receiving federal funds, in violation of 18 U.S.C. § 666(a)(2); and (3) conspiracy to violate the Hobbs Act, in violation of 18 U.S.C. § 1951. The district court granted Mr. Mitchell's motion for judgment of acquittal on the Hobbs Act charge, but a jury convicted Mr. Mitchell of the remaining two counts. The district court sentenced Mr. Mitchell to 97 months' incarceration and three years' supervised release. On appeal, Mr. Mitchell claims that the district court erred by instructing the jury that deliberate ignorance, in some instances, can constitute knowledge. He further asserts that the sentence imposed by the district court was procedurally and substantively unreasonable. Having reviewed the record, the parties' briefs and the applicable law, we now affirm the judgment of the district court.

I

BACKGROUND

A. Facts

Mr. Mitchell was a partner in the Cleveland, Ohio, law firm of Armstrong, Mitchell, Damiani and Zaccagnini ("AMDZ") from the early 1980s until 2006. His partners in the firm were Timothy Armstrong, Lou Damiani and Bruce Zaccagnini. There was no formal partnership agreement at AMDZ; each partner practiced in a different area of law, and each represented his clients with essentially no oversight. However, each partner shared evenly in the firm's profits. Damiani was the closest person the firm had to a managing partner because he was responsible for taking care of AMDZ's finances.

1. The Government's Case1

The AMDZ partnership structure was beneficial to Mr. Mitchell, who specialized in personal injury and medical malpractice cases. He would take these cost-intensive cases on a contingency-fee basis. By contrast, each of his partners billed by the hour. Because the partners split expenses and profits evenly, Mr. Mitchell was able to take on costly cases that he would not otherwise have been able to litigate while continuing to draw compensation regularly from his partners' fees during the pendency of such actions. In exchange, he would share his occasional "windfall" awards with his partners, who were effectively helping to finance his work. Mr. Mitchell often would admit to his partners that "but for the continuous payroll that w[as] coming from the other partners and associates in the firm, he wouldn't have been able to do that."2

Frank Russo was the elected auditor of Cuyahoga County, Ohio, which includes the City of Cleveland. Part of Russo's job as auditor was to oversee tax appraisals on properties within the County. In 1997, Damiani approached his partners in AMDZ about forming a business to solicit lucrative appraisal work from Russo, whom Damiani had known before Russo became auditor. On Damiani's suggestion, all four partners traveled to Atlantic City to meet with Robert Scrivens, a real estate appraiser. Although Mr. Mitchell and Zaccagnini met Scrivens in Atlantic City, they did not attend the meeting between him, Damiani and possibly Armstrong. When the partners were driving back from Atlantic City, Damiani explained that Scrivens was going to ask Joe Beres, another appraiser, to be involved with the enterprise. Damiani also indicated that he would speak with Russo and Sandy Klimkowski, an employee from the auditor's office, to "express an interest in" securing this contract.3 According to Zaccagnini, Damiani told the partners, including Mr. Mitchell, "that Frank [Russo] would want to, you know, be taken care of. You know, we're going to have to come up with cash for him as well," but that "`there is going to be plenty of money there and [that] it w[ould] still be lucrative for us.'"4

Upon their return, Damiani told Zaccagnini that the State of Ohio maintained a list of approved contractors and that, while they needed to be on that list, they needed to do so by forming a company that could not be traced to them. Zaccagnini and Armstrong then filed articles of incorporation for Valuation Advisory Services, Inc. ("VAS"), which listed Scrivens as the company's incorporator and shareholder. VAS then submitted an application to be on the Ohio Tax Commissioner's list, which was approved. Thereafter, Armstrong set up an office for VAS in downtown Cleveland. VAS employed a general manager to handle administrative matters in the office and to sign blank checks for Damiani and Zaccagnini.

At about the same time, Damiani approached Russo and Klimkowski about contracting with VAS. Russo and Damiani agreed on the terms of a contract, which was approved by the county commissioners. After one or two years, however, Russo learned that he could award these contracts to VAS without putting them out for bid and without seeking the commissioners' approval, which he did from then on. Russo and VAS would enter into "base" contracts at about the same amount as the previous agreement, but would then issue addenda to increase the amount "[b]ecause [Russo] never liked entering into contracts with big numbers all at once."5

The contracts between VAS and the County contained a fee schedule that called for VAS to be paid monthly. Zaccagnini, who drafted these agreements, testified that the amount VAS was to be paid was "[s]ignificantly more" than the legitimate expenses that VAS incurred in conducting appraisals and that the payment terms of the agreement had no "rational relevance or connection to the expenses of the contract."6 Klimkowski, who served as "the middle person between Frank Russo and Lou Damiani," would hand deliver these monthly payments to Damiani.7 Damiani and Klimkowski also would meet once a month so that Damiani could give Klimkowski an envelope containing $10,000 in $100 bills that was then passed on to Russo. This amount increased over time. In 2004, Damiani began to pay Klimkowski $3,000 per month as well, which eventually increased to $6,000 per month. When the scheme began, Damiani explained to Zaccagnini, Armstrong and Mr. Mitchell that they would need to come up with the money to pay Russo. Each partner was expected to put up one-fourth of this amount.

There was often a period of "drag time" between Damiani's receipt of the check from Klimkowski and Damiani's payments to Russo and Klimkowski.8 In the interim, Damiani would give the Klimkowski check to Zaccagnini, who would move the funds through various accounts before depositing into AMDZ's account the substantial amount that was left over after VAS's minimal expenses were paid.

Mr. Mitchell's wife filed for divorce in 2001. AMDZ was named a party to the divorce, and Mrs. Mitchell's attorneys sought discovery of the firm's financial records. Zaccagnini testified that there was a great deal of concern at AMDZ that someone might learn of the scheme during the divorce proceedings. Damiani told Mr. Mitchell that he "was concerned that this put everything at risk" because it could lead to someone discovering that "this money was eventually coming to the firm."9 Mr. Mitchell apologized and said, "[L]et's just do whatever we have got to do. Let's fight it."10 The divorce was eventually resolved by settlement, and the documents in question never were disclosed.

In 2005, Damiani learned that he had cancer. In March of 2006, Damiani informed Mr. Mitchell that he was terminally ill and that the VAS contract would be over once he died. Nevertheless, in June of 2006, Damiani told Zaccagnini that the scheme would in fact continue after his death with Zaccagnini taking over Damiani's leadership role and with Damiani's wife and Zaccagnini as the only participants on the VAS side of the arrangement. In August of that year, Damiani brought Zaccagnini to his monthly rendezvous with Klimkowski. He told her, "What you did with me, you'll do with Bruce [Zaccagnini,]... [a]nd the conditions w[ill] stay the same with everybody."11 Damiani passed away within the next week. Thereafter, Klimkowski would deliver the checks to Zaccagnini, and he would provide her, in turn, with the envelopes filled with cash.

Zaccagnini began distributing the partners' checks and collecting the bribe money in September of 2005, nearly a year before Damiani ultimately passed away.12 When Damiani was still participating actively in the scheme, Zaccagnini would then deliver the bribe money to Damiani. Zaccagnini testified that, once he began collecting the bribe money, he would write the amount he needed from each partner on a Post-it note attached to each partner's draw check. Mr. Mitchell was typically prompt, and was often early, in providing his portion of the cash to Zaccagnini. On one occasion, Mr. Mitchell either had forgotten that he had received a draw check or had misplaced it, and he was accordingly late with his payment. Upon finding the check, he immediately paid his share to Zaccagnini.

After Damiani's death, Zaccagnini told Armstrong and Mr. Mitchell that the VAS contract was over. As we noted above, this was a lie; the contract was still in force with Zaccagnini and Damiani's widow. Indeed, Damiani had negotiated a new contract with Russo shortly before he died, and he instructed Zaccagnini to finish out that contract but not to negotiate a new one thereafter. Mr. Mitchell expressed an interest in continuing the contract, but Zaccagnini said that Russo and Klimkowski would not deal with him.

At around that same time, AMDZ was winding down its business; AMDZ had lost Damiani to cancer and was about to lose Armstrong to a solo practice. Zaccagnini then announced that he would be leaving the firm as well, and AMDZ dissolved at the end of 2006.

In November 2007, Mr. Mitchell called Zaccagnini. He expressed his displeasure with Russo for passing over his son-in-law for a job. Zaccagnini said he did not know anything about this, and Mr. Mitchell replied, "`Look, we all know all you got to do is pay Frank Russo and you can get a job.'"13 The two then got together, and Mr. Mitchell said that Damiani "screwed up" by letting the VAS contract go.14 When Zaccagnini lied and said that Scrivens — the appraiser from Atlantic City — was the one getting all the money now, Mr. Mitchell replied, "`He needs to help out. He shouldn't be getting all that money.'"15 Mr. Mitchell said that he and his new wife were borrowing heavily on their credit cards and that they were "`zapped.'"16

Zaccagnini continued the scheme until July of 2008, when the FBI searched the Cuyahoga County Administration Building in connection with an investigation into various crimes involving public officials and private contractors. Shortly thereafter, in August of 2008, Mr. Mitchell met with Zaccagnini. Mr. Mitchell suggested that Russo was "done" and that they should run Mr. Mitchell's son-in-law to replace Russo so that Klimkowski "would have job security and" so they could "`get the contract back with VAS.'"17 Mr. Mitchell then suggested that if the FBI's investigation turned to VAS, they should "`blame it all on Armstrong,'" who had been involved with VAS's work.18 Zaccagnini replied that "`we're the one[s] that got the money and paid the bribes'" and that "`[t]here is a paper trail.'"19 Mr. Mitchell said that Zaccagnini should "`just let [him] do the talking.'"20

2. Mr. Mitchell's Defense

Mr. Mitchell testified in his own defense, contradicting a great deal of the foregoing facts. He denied knowing about or participating in a scheme to bribe Russo or Klimkowski. He also denied ever hearing that Russo needed "to be taken care of."21 He further denied telling Zaccagnini that they should blame everything on Armstrong if they were investigated. As to his divorce, Mr. Mitchell testified that all of the partners were upset and that Damiani was trying to avoid being deposed, although none of the partners ever told Mr. Mitchell that they were trying to avoid discovery "because they were doing this stuff."22

According to Mr. Mitchell, Damiani "told [him] one day that [they] were going to have a client [from New Jersey] who was going to do real estate appraisals."23 Mr. Mitchell testified that he indicated simply that this "[s]ound[ed] good."24 He explained that his reason for going to Atlantic City was "to have some fun" with Scrivens, whom he had known for years.25 He further testified that he never heard of VAS until around 2004 and that he assumed "that was the real estate appraisal company [they] were representing," but that he never talked with anyone about VAS.26

On cross-examination, Mr. Mitchell testified that he often would get between $3,000 and $8,000 in cash when he would deposit his draw checks from AMDZ and that he "always carried a big wad of cash."27 However, he denied ever giving any cash to Russo or Zaccagnini.

B. District Court Proceedings

After a week-long trial, the district court submitted the case to the jury on two counts:28 conspiracy to commit bribery concerning programs receiving federal funds, and bribery concerning programs receiving federal funds. At the Government's request, and over Mr. Mitchell's objection, the district court included the following instruction:

The jury returned a general verdict of guilty on both counts.

A presentence investigation report ("PSR") was then prepared. The PSR calculated Mr. Mitchell's base offense level as 12.30 Two levels were added because the offense involved more than one bribe.31 Sixteen levels were added because Mr. Mitchell received over $1,000,000 in return for the payments to the public official.32 Finally, four levels were added because the offense involved a bribe to an elected official.33 Then, two levels were subtracted for Mr. Mitchell's role in the offense being minor.34 Therefore, the PSR concluded that Mr. Mitchell's adjusted offense level was 32. Because his criminal history category was I, the PSR concluded his guidelines range was 121-151 months' imprisonment. The PSR noted, however, that the conspiracy count carried a statutory maximum of 60 months and that the bribery count carried a statutory maximum of 120 months.35

At his sentencing hearing, Mr. Mitchell objected that his two-level reduction for a "minor" role actually should have been a four-level reduction because his role was "minimal." The Government consented to the four-level reduction "[i]n order to be consistent with" Armstrong's sentence.36 Although the district court did not believe "that either of these two gentlemen were really minimal participants,"37 it accepted the concession to minimize any disparity between Armstrong's and Mr. Mitchell's sentences.

Mr. Mitchell also requested a departure under U.S.S.G. § 5H1.6 based on his "family ties and responsibilities."38 He noted that his wife had undergone two surgeries for breast cancer, had no medical insurance, owed $250,000.00 in medical bills and is unemployable. He further noted that he and his wife were in bankruptcy. The district court determined that such a departure was not warranted because there was nothing in the record that would suggest that Mr. Mitchell could ameliorate his wife's situation if his term of incarceration were shortened.

The district court concluded that Mr. Mitchell's adjusted offense level was 30 and that his criminal history category was I. It determined that the proper guidelines range for Mr. Mitchell was 97 to 120 months, taking into account the ten-year statutory maximum.

The district court then turned to the sentencing factors outlined in 18 U.S.C. § 3553(a). The court found that Cuyahoga County paid VAS over $12,000,000 through this scheme and that Mr. Mitchell had paid kickbacks to Russo, earning over $1,000,000 for himself in the process. The court then described Mr. Mitchell's history and characteristics, noting particularly Mr. Mitchell's wife's health issues and the Mitchells' "financial straits."39 Turning to the factors in § 3553(a)(2), the court concluded that the multi-year, multi-million dollar offense affected the citizens of Cuyahoga County financially and was "an affront to our system and the trust that we place in our public officials," particularly because Mr. Mitchell was an attorney who "t[ook] an oath to uphold the laws."40 The district court concluded that this, along with the other factors listed in § 3553(a)(2), "warrant[ed] a substantial sentence" within the guidelines range.41

However, the district court indicated that it was "well aware of its duty not to create an unwarranted sentencing disparity among defendants with similar records who have been found guilty of similar conduct."42 It referenced a chart that indicated that the median term of imprisonment for defendants convicted of bribery was 21.0 months nationally and 22.5 months in the Northern District of Ohio, but it concluded that the chart "doesn't control in this case" because "[t]here's nothing to indicate" that the numbers in the chart reflect the "unique situation" at hand — i.e., multiple bribes paid to a public official to obtain a large benefit.43 Instead, the court looked to Armstrong, who the court determined was the AMDZ partner who was most similar to Mr. Mitchell in terms of culpability. Armstrong was sentenced to 42 months' imprisonment after providing "very complete"44 cooperation in a conspiracy case that otherwise would have been difficult to prove. The district court noted that if Armstrong would not have accepted responsibility and cooperated with the investigation and prosecution of the VAS conspiracy, his guidelines range would have been 78 to 97 months. The court further noted that the judge who sentenced Armstrong considered Armstrong's "lifetime of good works" in determining an appropriate sentence for him, something that the district court found to be "not present in this case."45 In the end, the district court employed a two-level downward "variance," which yielded an offense level of 28 and a corresponding guidelines range of 78 to 97 months' imprisonment.46 The district court therefore proceeded as if Mr. Mitchell's guidelines range was identical to what Armstrong would have faced had he not cooperated and accepted responsibility.47

Considering that Mr. Mitchell was a partner in a law firm, with an ethical duty to know how his law firm was being operated, and that he was attempting to "more than minimize"48 his involvement in the scheme,49 the district court concluded that a sentence at the high end of the modified guidelines range was appropriate. Therefore, the court sentenced Mr. Mitchell to 97 months' imprisonment to be followed by three years' supervised release, in addition to $1,120,000 in restitution. The court held that Mr. Mitchell's wife's condition did not justify a variance "for the same reason [the court] stated previously."50

II

DISCUSSION

A. Deliberate Ignorance Instruction

Mr. Mitchell first challenges the district court's instruction to the jury on deliberate ignorance. We review challenges to a jury instruction for an abuse of discretion. United States v. Williams, 612 F.3d 500, 506 (6th Cir.2010). "[N]o single provision of the jury charge may be viewed in isolation; rather, the charge must be considered as a whole." United States v. Ross, 502 F.3d 521, 527 (6th Cir.2007). Therefore, "[w]hen jury instructions are claimed to be erroneous, we review the instructions as a whole, in order to determine whether they adequately informed the jury of the relevant considerations and provided a basis in law for aiding the jury in reaching its decision." United States v. Frederick, 406 F.3d 754, 761 (6th Cir. 2005). "A trial court has broad discretion in crafting jury instructions and does not abuse its discretion unless the jury charge fails accurately to reflect the law." United States v. Geisen, 612 F.3d 471, 485 (6th Cir.2010). An improper instruction requires reversal of the judgment "only if the instructions, viewed as a whole, were confusing, misleading, or prejudicial." United States v. Kuehne, 547 F.3d 667, 679 (6th Cir.2008) (internal quotation marks omitted).

Mr. Mitchell concedes that the deliberate ignorance instruction, which was derived from Sixth Circuit Pattern Instruction 2.09, accurately stated the law.51 Nevertheless, he submits that the instruction presented an unacceptable risk of misleading the jury. To evaluate his contention, we must scrutinize the instructions as a whole and determine whether, when read in their entirety, they misled the jury.

This is not, of course, our first encounter with this instruction. Our case law makes clear that the decision to give this instruction is to be approached with significant prudence and caution. More specifically, we have noted that the instruction should not be given routinely because of the risk of a conviction based on mere negligence, carelessness or ignorance. United States v. Mari, 47 F.3d 782, 785 (6th Cir.1995). Indeed, we have said that the instruction ought to "be used sparingly." Geisen, 612 F.3d at 486.

The disputed instruction, sometimes called the "ostrich instruction,"52 is designed for a very specific situation. The instruction explains to the jury that knowledge, within the meaning of the statute, also includes the deliberate avoidance of knowledge. It is appropriate when: (1) the defendant claims a lack of guilty knowledge; and (2) the facts and evidence support an inference of deliberate ignorance. Before giving the instruction, the district court therefore must determine that there is evidence to support an inference "that the defendant acted with reckless disregard of [the high probability of illegality] or with a conscious purpose to avoid learning the truth." United States v. Seelig, 622 F.2d 207, 213 (6th Cir.1980) (internal quotation marks omitted); see also Geisen, 612 F.3d at 487-88 (concluding that a deliberate ignorance instruction was appropriate where evidence established that the defendant "deliberately chose not to inform himself" of the critical facts); United States v. Stone, 9 F.3d 934, 937 (11th Cir.1993) ("A deliberate ignorance instruction is appropriate only when there is evidence in the record showing the defendant purposely contrived to avoid learning the truth." (internal quotation marks omitted)). "Deliberate avoidance is not a standard less than knowledge; it is simply another way that knowledge may be proven." United States v. Severson, 569 F.3d 683, 689 (7th Cir.2009). Deliberate ignorance "can be the result of a mental, as well as physical effort — a cutting off of one's normal curiosity by an effort of will." United States v. Hoyos, 3 F.3d 232, 237 (7th Cir.1993) (internal quotation marks omitted). To permit a conviction without proof of actual knowledge or deliberate, willful avoidance of that knowledge would simply erase the knowledge requirement from the statute. See United States v. Heredia, 483 F.3d 913, 926 (9th Cir. 2007) (en banc) (Kleinfeld, J., concurring). In short, "this instruction, like all instructions, should be given only when it addresses an issue reasonably raised by the evidence." United States v. Diaz, 864 F.2d 544, 549 (7th Cir.1988).

Mr. Mitchell argues that the deliberate ignorance instruction should not have been given because the factual predicate that we have just described was not present. As he sees it, the basic issue before the jury was whether he gave bribe money to Damiani and Zaccognini. He contends that the evidence at trial demonstrated that he did not give a bribe because there was no credible evidence that such a bribe was in fact given. Therefore, in his view, the question of his knowledge, or lack of knowledge, of such a bribe was not at issue. Consequently, he argues, the concept of deliberate ignorance is totally irrelevant to the issue at hand. Its introduction into the jury's deliberations confused and misled it into believing that the act of his giving money must have occurred and that the only issue it had to decide was whether Mr. Mitchell knew what Zaccognini and Damiani were going to do with that money.

The Government, both at trial and on appeal, presents a different view of the evidence. It submits that the evidence not only showed that bribes had been given to Russo, but also that Mr. Mitchell knew that the bribes had been given and that he knowingly participated in the giving of the bribes. To secure a conviction, then, it was essential to establish Mr. Mitchell's state of mind and prove that he knowingly joined the conspiracy and that he knowingly participated in giving the bribe to Frank Russo with the intent to influence or reward him for awarding the County contract to VAS.

Both parties had the right to have the case submitted to the jury under instructions that would allow a full and fair evaluation of the evidence of record in light of the theories proffered by each side. Here, there was evidence that Damiani explicitly told Mr. Mitchell that Russo would have to "be taken care of."53 Zaccognini, who testified that he was present during the conversation, told the jury that he had understood that Damiani was talking about bribing Russo. Armstrong also testified that he understood that the VAS contract was dependent on cash bribes to Russo and that all four partners of the law firm, including Mr. Mitchell, had contributed to that bribe on a monthly basis for nine years. Mr. Mitchell, while denying that he knew of or participated in the bribery scheme, did admit that he had accepted the proceeds from the VAS contract for nine years. He testified that he thought the trip to Atlantic City — where, according to his partners, the foundation for the VAS scheme was set up — was just a trip "to have some fun"54 and that, when he found out about the existence of VAS in 2004, he thought it was just a client whose business had been brought into the firm by one of his partners. He testified that he hardly talked at all to Armstrong and that Damiani "was not the kind of person who would tell you what he was doing."55 Indeed, he continued, "I wouldn't talk to him... that much as time went on."56 Furthermore, although he denied that his divorce should have been a matter of any concern to the law firm, he acknowledged that his partners were upset about it. Although both Zaccognini and Armstrong testified that resolution of the divorce proceeding was a matter of concern to the firm because there was a fear that an investigation of Mr. Mitchell's income and its sources would disclose the firm's association with the VAS contract, Mr. Mitchell claimed that, when he inquired about their concern, they said nothing about such a possible disclosure.

Given this evidence, the jury was confronted with three basic options. First, it could have believed that Mr. Mitchell was involved in the bribery scheme and that his testimony to the contrary was simply a lie. Second, the jury could have believed Mr. Mitchell's testimony that he profited unwittingly from the VAS bribery scheme because the distribution of its profits was made through the law firm partnership draw, an arrangement in which all partners shared equally and not as a function of their own billing, and that he had no knowledge of the scheme and had not contributed to the scheme. Third, the jury could have concluded that Mr. Mitchell, despite his testimony to the contrary, had given money to Zaccognini or Damiani but did not actually know that Damiani was bribing Russo on behalf of the firm's partners because he deliberately avoided such knowledge by insulating himself from the day-to-day mechanics of the bribery scheme.

There was clearly evidence of record to support this last theory. Mr. Mitchell had been a long-time partner in the law firm, with access to its accounts, and could have discovered the nearly decade-long bribery scheme rather than just accepting the inflated draw on a regular basis. In the face of that evidence, he testified that, despite his long tenure in the firm, he paid little attention to the clients of his partners and knew little about the actual running of the law firm. Therefore, he accepted the payments without knowing where they were coming from. After all, profits were divided equally among the partners. He was content to accept his partners' reticence on the sources of his firm's income. As his counsel described him to the jury, "[h]e did what he did well, and he didn't care what anyone else did. People didn't stick their nose[s] in his business, and he did not stick his nose in other people's business."57 He therefore placed before the jury the possibility that his lack of knowledge was due to negligence or inadvertence and not an attempt to turn deliberately a blind eye to an ongoing illegality.58

Faced with this possibility, it was incumbent on the Government to rebut that evidence and to argue to the jury a competing theory — that Mr. Mitchell had avoided deliberate knowledge of the particulars of the scheme (such as the manner in which Russo was to "be taken care of"59) in order to insulate himself from criminal liability. Moreover, because this theory was put in play by the evidence submitted by the parties, it was certainly within the sound discretion of the district court to address that evidence and the competing theories in its instructions.

We further note that the instruction actually given by the district court to address this aspect of the case was well-suited to the situation presented by this case. First, in its opening sentence, the instruction states explicitly that criminal liability attaches only by "deliberately ignoring the obvious." Sixth Circuit Pattern Jury Instruction 2.09 (emphasis added). Second, it requires — explicitly — that the jury "be convinced beyond a reasonable doubt that the defendant ... deliberately closed his eyes to what was obvious." Id. (emphasis added). Third, the instruction pointedly and explicitly states that carelessness, negligence and foolishness are not the same as knowledge and are not sufficient to convict. It therefore explicitly cautions the jury not to fall into the trap, repeatedly identified in our case law, of convicting on the basis of a mental state that is something less than knowledge. Finally, we note that we have approved the giving of this instruction "`to show a conspirator's knowledge of the unlawful aims of a conspiracy.'" Williams, 612 F.3d at 508 (quoting United States v. Warshawsky, 20 F.3d 204, 210 (6th Cir.1994), superseded on other grounds as stated in United States v. Myint, 455 Fed.Appx. 596, 604 (6th Cir.2012)).

B. Sentencing

Mr. Mitchell raises also various objections to the sentence imposed by the district court. We review his sentence for reasonableness, both procedural and substantive, for an abuse of discretion. Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007); United States v. Cunningham, 669 F.3d 723, 728 (6th Cir.2012). We

Gall, 552 U.S. at 51, 128 S.Ct. 586; see also Cunningham, 669 F.3d at 728 ("Procedural reasonableness review begins with a robust review of the factors evaluated and the procedures employed by the district court in reaching its sentencing determination." (internal quotation marks omitted)). We then consider the substantive reasonableness of the sentence under the totality of the circumstances. Gall, 552 U.S. at 51, 128 S.Ct. 586. "A sentence is substantively unreasonable if the sentencing court arbitrarily selected the sentence, based the sentence on impermissible factors, failed to consider pertinent § 3553(a) factors, or gave an unreasonable amount of weight to any pertinent factor." Cunningham, 669 F.3d at 733. We give deference to the district court's sentence to the extent it is justified by the § 3553(a) factors, and we may presume that a within-guidelines sentence is reasonable. Id.

1. Procedural Reasonableness

Mr. Mitchell contends that the district court erred by failing to depart downward60 under United States Sentencing Guideline § 5H1.6, the policy statement regarding family ties and responsibilities. This error, according to Mr. Mitchell, resulted in a miscalculation of the applicable guidelines range. Nevertheless, "we have consistently held that the decision by a district court not to depart downwards from the Guidelines is not reviewable on appeal unless the record reflects that the district court was not aware of or did not understand its discretion to make such a departure." United States v. Puckett, 422 F.3d 340, 344 (6th Cir.2005) (internal quotation marks omitted); see also id. at 345 (concluding that this rule survived United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005)). In this case, the district court indicated that it had considered the factors relevant to United States Sentencing Guideline § 5H1.6 and determined that the departure was not warranted. See R.59 at 9 ("[T]he court finds based upon the information that it has before it, that this departure does not apply."); id. ("[T]here's just simply not anything in this record [that] would meet any of the factors that the court is to consider under 5H1.6 in applying this particular departure, so the court, therefore, will not apply that departure."). Accordingly, this assignment of error is not reviewable.

Similarly, Mr. Mitchell asserts that the district court committed procedural error by failing to explain adequately its reasons for denying his request for a downward variance based on his wife's medical condition. "In order for a district court's sentencing determination to be procedurally reasonable, a `sentencing judge should set forth enough to satisfy the appellate court that he has considered the parties' arguments and has a reasoned basis for exercising his own legal decision-making authority.'" United States v. Gapinski, 561 F.3d 467, 474 (6th Cir.2009) (quoting Rita v. United States, 551 U.S. 338, 356, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007)). Although we cannot review the district court's decision not to depart downward based on Mr. Mitchell's wife's health condition, we are obligated to ensure that the court explained adequately its reasons for choosing not to grant a variance on that basis.61

At sentencing, Mr. Mitchell contended that the district court either should have departed or applied a downward variance because his wife was very ill and did not have the financial resources necessary to pay for the costly course of treatment required by her illness.62 The district court determined that a variance was not appropriate based on Mr. Mitchell's wife's medical condition "for the same reason" that it did not believe a departure was warranted.63 The court previously had explained that it did not believe that a departure was appropriate for the following reasons:

It is clear from the sentencing transcript that the district court's reason for denying Mr. Mitchell's request for a variance was that Mr. Mitchell's conduct, in its view, merited a substantial prison sentence and that there was nothing in the record to suggest that imposing a shorter sentence would allow Mr. Mitchell to provide the financial support that his wife needed. Accordingly, we are satisfied that the district court responded to Mr. Mitchell's argument for a downward variance and explained adequately why it did not believe that such a variance was justified. The district court "set forth enough to satisfy [us] that [it] ... considered [Mr. Mitchell's] argument[] and ha[d] a reasoned basis for exercising [its] own legal decision-making authority." Rita, 551 U.S. at 356, 127 S.Ct. 2456; see also United States v. Herrera-Zuniga, 571 F.3d 568, 587 (6th Cir.2009) ("Although the sentencing court is required to provide an adequate explanation of the basis for its decision, the court may exercise discretion in determining how much of an explanation of the sentence is required because the amount of reasoning required varies according to context." (internal quotation marks omitted)).

Mr. Mitchell's final argument regarding the procedural reasonableness of his sentence fares no better. He asserts that the district court failed to vary downward to prevent an unwarranted sentencing disparity with Armstrong, even though the court determined that such a variance was appropriate in this case. We cannot accept this argument. In order to prevent an unwarranted sentencing disparity between Mr. Mitchell and Armstrong, whom the district court found to be similarly culpable co-conspirators, the court indicated that it would select Mr. Mitchell's sentence from the guidelines range that Armstrong would have faced had he not received a downward departure for acceptance of responsibility. In that regard, the court exercised its authority under § 3553(a) to "vary" from Mr. Mitchell's advisory guidelines range to Armstrong's range. Because the court found that a sentence at the "high end of the range [wa]s appropriate" after it weighed the § 3553(a) factors,65 it sentenced Mr. Mitchell to 97 months' imprisonment, the highest sentence available within Armstrong's advisory range. And, because Mr. Mitchell could have received 97 months if he had been sentenced at the very lowest level within his guidelines range, he asserts that the district court did not give him the "variance" it had determined to be appropriate.

It is apparent that the district court and Mr. Mitchell are using the term "variance" to mean two different things. Mr. Mitchell is using the term in the traditional sense, which "refers to the selection of a sentence outside of the advisory Guidelines range based upon the district court's weighing of one or more of the sentencing factors of § 3553(a)." United States v. Denny, 653 F.3d 415, 419 (6th Cir.2011) (internal quotation marks omitted). The district court, on the other hand, was using the term to indicate that it was considering a range of sentences outside of Mr. Mitchell's guidelines range — i.e., that it was varying the range from which it would select Mr. Mitchell's sentence. Nothing in the sentencing transcript suggests that the district court determined conclusively that a sentence below Mr. Mitchell's guidelines range was necessary. Rather, the district court made it clear that it was merely considering the possibility of doing so. We would be elevating form over substance if we were to conclude that the district court committed reversible error by using a term of art imprecisely where, as here, the underlying basis for the court's determination is perfectly clear from the record. Cf. id. at 420 (reiterating "that no specific magic words are necessary to render a sentence reasonable" and looking to the context in which the district court used the term "departure" to conclude that the district court obviously was discussing a "variance" (internal quotation marks omitted)).

Having found each of Mr. Mitchell's claims of procedural unreasonableness to be without merit or unreviewable, we conclude that Mr. Mitchell has not established that his sentence was procedurally unreasonable.

2. Substantive Reasonableness

a. Sentencing Disparity

Mr. Mitchell asserts that his sentence was substantively unreasonable because it "created a substantial sentencing disparity in contravention of 18 U.S.C. [§ ] 3553(a)(6)." Appellant's Br. 57. "We have explained[] ... that this factor concerns national disparities between defendants with similar criminal histories convicted of similar criminal conduct — not disparities between codefendants." United States v. Conatser, 514 F.3d 508, 521 (6th Cir.2008) (emphasis in original). Mr. Mitchell notes that the national average sentence for a bribery conviction (21 months) is substantially lower than the sentence he received (97 months). However, Mr. Mitchell received a within-guidelines sentence.

United States v. Swafford, 639 F.3d 265, 270 (6th Cir.2011) (emphasis in original) (citing United States v. Shrake, 515 F.3d 743, 748 (7th Cir.2008)). Therefore, this disparity does not render Mr. Mitchell's within-guidelines sentence substantively unreasonable. See United States v. Benson, 591 F.3d 491, 505 (6th Cir.2010).

The heart of Mr. Mitchell's disparity argument, however, is that his sentence (97 months) is unreasonably high in comparison to Zaccagnini's (60 months) and Armstrong's (42 months). Although the district court was not required to consider this issue, United States v. Simmons, 501 F.3d 620, 624 (6th Cir.2007), it exercised its discretion to do so. To that end, the court first determined that Armstrong was similarly culpable to Mr. Mitchell and, accordingly, that it should attempt to prevent an unwarranted discrepancy between these two co-conspirators. Mr. Mitchell asserts here, as he did before the district court, that Armstrong was actually more culpable than he was because Armstrong helped draft the initial VAS contract and had appraisal experience. The district court rejected that argument, emphasizing that both Armstrong and Mr. Mitchell were present on the trip to Atlantic City when the plan was first set in motion and that they both paid the kickbacks and received the payments over a period of several years.66 Mr. Mitchell has failed to establish that the district court's conclusion on this point was an abuse of discretion. See United States v. Bacon, 617 F.3d 452, 459-60 (6th Cir.2010).

After determining that Armstrong's culpability was similar to Mr. Mitchell's, the district court noted that Armstrong accepted responsibility for his conduct and provided very complete cooperation from early on in the investigation. The district court attempted to account for this difference by choosing Mr. Mitchell's sentence from the advisory range that Armstrong would have confronted had he not cooperated. Furthermore, the district court already had given Mr. Mitchell the four-level departure for being a minimal participant, rather than the two-level departure for being a minor participant recommended by the PSR, to guard against a disparity claim. It did so even though it considered neither Armstrong nor Mr. Mitchell to be minimal participants, as that term is used in the guidelines.

Because a disparity that results from a co-conspirator's cooperation is not an "unwarranted sentence disparit[y]" within the meaning of § 3553(a)(6), see United States v. Vowell, 516 F.3d 503, 513 (6th Cir.2008), it was not unreasonable for the district court to attempt to take these differences into account. See United States v. Stewart, 628 F.3d 246, 260 (6th Cir.2010) ("Stewart, in contrast [to his co-defendants], did not cooperate with the government or accept responsibility for his actions, and thus did not warrant any leniency on these grounds."). Nor was it unreasonable for the district court to address the issue in the way that it did. The court gave Mr. Mitchell the benefit of a guidelines adjustment that it did not believe was appropriate to ensure parity between Mr. Mitchell and the hypothetical sentence that Armstrong would have faced; it then considered sentences below that already artificially low guidelines range for the sole purpose of treating Mr. Mitchell the way that Armstrong was likely to have been treated but for his cooperation. Of course, there was no way for the court to know the exact sentence that Armstrong would have received had he not cooperated. However, it was not unreasonable for the district court to look to the guidelines range that Armstrong would have faced in an attempt to create a counterfactual sentence to which Mr. Mitchell's sentence could be compared.

The district court went out of its way to prevent an unwarranted sentencing disparity between Mr. Mitchell and Armstrong, and Mr. Mitchell is hard-pressed to challenge on appeal this favorable treatment. Indeed, we conclude that Mr. Mitchell has failed to establish that the district court abused its discretion by failing to go further than it did in attempting to address the possibility of an unwarranted sentencing disparity between Mr. Mitchell and his co-conspirators.

b. § 3553(a) Factors

Mr. Mitchell's final argument on appeal is that his within-guidelines sentence is substantively unreasonable because the district court gave what he considers to be an unreasonable amount of weight to his failure to take responsibility for his actions and his lack of remorse. A significant aspect of his argument is that he was not involved in the bribery scheme and that he cannot take responsibility for something that he did not do. He also contends that he "already los[t] the three[-]level reduction for acceptance of responsibility that [he] would have received for pleading guilty" and that "[h]e should not receive a defacto [sic] penalty for exercising his right to a jury trial." Appellant's Br. 56. However, the jury found that Mr. Mitchell had participated in the conspiracy, and the district court indicated that it agreed with that determination. Therefore, the district court found that Mr. Mitchell's continued efforts to deny his involvement demonstrated a failure to take responsibility for his crime and a lack of remorse for the harm he had caused. "The judge could have reasonably concluded that [Mr. Mitchell]'s dishonesty regarding important pieces of evidence indicated that he had not fully accepted responsibility for his participation in the conspiracy." United States v. Sutton, 387 Fed.Appx. 595, 607 (6th Cir.2010). Accordingly, "it was not [Mr. Mitchell]'s exercise of his right to [a jury trial], but rather, that he did not accept responsibility for his crime, that the district court took into account in considering the § 3553(a) factors. This was not error." United States v. Delano, 411 Fed.Appx. 795, 799 (6th Cir.2011).

Furthermore, we conclude that the district court did not give an unreasonable amount of weight to any one factor. As noted above, the court went to great lengths to consider the need to avoid unwarranted sentence disparities among the co-conspirators. Additionally, in considering the seriousness of the offense, the court noted that even though Mr. Mitchell was trained in the law and had taken an oath to uphold the law, he nevertheless conspired with his partners, who were also lawyers, to defraud the people of Cuyahoga County of their tax dollars with no regard to the effect that this scheme would have on the trust that the citizens of the County place in their elected officials. The court stated that, in addition to the seriousness of the offense, these facts also went to the "need to promote respect for the law, provide just punishment for the offense and afford adequate deterrence to others."67 All of this, the court concluded, made the modified guidelines range that it had constructed to prevent an unwarranted disparity with Armstrong "an appropriate range considering all the factors that the court is to consider."68 It was only then, in considering what sentence within that range would be most appropriate, that the court noted that Mr. Mitchell failed to express remorse and continued to deny responsibility. After taking into account "all of the sentencing factors the court must consider and specifically the ones noted" above, the court then concluded that a sentence at the "high end of the range [wa]s appropriate."69 Thus, Mr. Mitchell's failure to take responsibility and lack of remorse were two facts that the court considered in weighing the various § 3553(a) factors that it found to be most relevant to the case at hand. This was not unreasonable.70 Accordingly, Mr. Mitchell has failed to rebut the presumption of reasonableness that attached to his within-guidelines sentence.

Conclusion

Because the district court's decision to instruct the jury on deliberate ignorance was not reversible error, and because the sentence imposed by the district court was neither procedurally nor substantively unreasonable, we AFFIRM the judgment of the district court.