FLAUM, Circuit Judge.

Ricky Boros, also known as Vince Kwiatkowski, appeals his convictions for conspiracy to import controlled substances, conspiracy to possess controlled substances with the intent to distribute, and conspiracy to launder money with the intent to promote the importation of controlled substances. The sole argument that he makes on appeal is that the district court erred by admitting the expert testimony of pharmacologist Dr. Robert Barkin. Dr. Barkin testified about the classification of various drugs, their side effects, and the medical supervision needed to prescribe them. Boros contends that this evidence was not relevant as defined by Federal Rule of Evidence 401 and that its admission was not harmless. We disagree. Although the testimony had only minimal relevance, the threshold for relevance under Rule 401 is quite low. The parts of the testimony related to side effects and birth defects, however, should have been excluded under Rule 403. Because the probative value was negligible, this testimony's potential for unfair prejudice to Boros should have tipped the scales in favor of exclusion. Nonetheless, we find this error to be harmless given the weight of the government's evidence. We therefore affirm the judgment of the district court.

I. Background

A. Factual Background

Boros, along with Larry and Gary Calow,1 founded an Internet pharmacy business in March 2003, which they incorporated in Belize under the name Purchase Meds, Inc. ("PMeds").2 PMeds sold prescription drugs, including controlled substances, to customers via its website, PMeds.com. A handwritten "letter of intent" memorialized its formation, the initial distribution of shares, and the roles of the founders. Boros assumed the role of corporate secretary. The Calows worked from Mexico and Tinley Park, Illinois, and Boros worked from his home in Oak Brook, Illinois. By 2006, PMeds had gross sales in excess of $5.5 million.

Although the website took orders for prescription medication, it did not require customers to have prescriptions. As of April 14, 2003, the website stated, "[I]f you do not supply a prescription, we will supply a prescription at no cost to you." As of June 27, 2004, the website promised to provide a "free online consultation with a licensed U.S. physician" to obtain prescription medication. The website required purchasers of controlled substances to disclaim their affiliation with government and news agencies. PMeds disclaimed responsibility for confirming importation regulations and placed the risk of loss on customers unless U.S. Customs provided seizure notification and proof of reclaim.

Boros's responsibilities for PMeds included advertising, directing website traffic, analyzing sales and inventory, negotiating prices with distributors, and obtaining prescriptions for orders stopped at the U.S.-Mexico border. Boros sent several emails to the Calows in 2003 and 2004 that referenced drug sales, including the sale of controlled substances. A spreadsheet attached to one of the emails listed the names and quantities of 235 products, including controlled substances, that PMeds had sold in the last three months. Boros picked up checks for PMeds on a weekly basis from the Tinley Park office, deposited them into his account, and gave the cash to Gary. Boros also received cash payments. His active participation with PMeds appears to have ended in mid-2004.

Joshua Morrow and Angela Burdick both worked for PMeds and later served as witnesses for the government. Morrow was initially a customer of PMeds and then started smuggling drugs for PMeds. He was arrested in 2005 for attempting to drive 200 packages of drugs into the United States. Burdick worked for PMeds in 2003 and was given a grant of immunity in exchange for her testimony about PMeds and the defendants' activities.

In 2006, the Drug Enforcement Administration ("DEA") conducted several undercover purchases of controlled substances through PMeds's website. In October 2006, law enforcement officers, accompanied by a DEA forensic chemist, executed a search warrant at the Tinley Park office and found flasks, spa oil bottles, a vacuum pump, and a vacuum filter flask. Forensic testing detected numerous types of steroids. In January 2007, Mexican police searched Alfa Pack Shipping Services in Metepec, Mexico, and found an invoice for spa oil bottles to be shipped from Gary's wife to Larry in Tinley Park. Further, IRS Special Agent William Desmond reviewed the records of the two bank accounts associated with PMeds. He found that fifteen credit card companies had transferred more than $5.5 million into the two accounts between May 15, 2003 and December 4, 2006, that nearly $2.5 million was wired from these accounts to Latin America, and that $47,074.32 was wired from these two accounts to Boros between December 30, 2003 and July 16, 2004.

On August 8, 2007, a grand jury returned a superseding indictment3 against Boros and five other defendants for conspiracy to import Schedule II, III, and IV controlled substances, in violation of 21 U.S.C. § 963 and 18 U.S.C. § 2; conspiracy to possess controlled substances with the intent to distribute, in violation of 21 U.S.C. § 846 and 18 U.S.C. § 2; money laundering, in violation of 18 U.S.C. § 1957 and 18 U.S.C. § 2; and conspiracy to launder money out of the United States with the intent to promote the importation, possession, and distribution of controlled substances, in violation of 18 U.S.C. § 1956 and 18 U.S.C. § 2. The government subsequently dismissed the substantive money laundering charges.

B. Procedural Background

The government disclosed prior to trial that it intended to call Dr. Barkin, a clinical pharmacologist, as an expert witness in clinical pharmacy. Boros filed a motion in limine to bar this testimony, arguing that evidence about the dangers of taking controlled substances without medical supervision "is a scare tactic without probative value." The district court found the motion to be untimely but still expressed some reservations:

The district court placed the onus on the defense to object if it perceived the testimony to cross the line established by the evidentiary ruling.

After the government tendered Dr. Barkin as an expert, Boros's counsel reminded the court of its pre-trial ruling and the court held a sidebar. Boros's counsel argued that Dr. Barkin should not "be out there raising prejudices about how terrible it is to take medicines without a prescription, that there's danger in taking medicine without a prescription, because that's got nothing to do with what we're on trial for." The government responded that Dr. Barkin would "address a number of controlled substances that PMeds dealt with, and talk about them, and the need for medical supervision and prescriptions, and the effects on people." The court viewed the matter as a question of "for how long and in what detail are we going to wallow in it" and held that "the jury is entitled to know, without going ... into great, great detail on this, why these subjects are regulated and what the issues are about them.... I think if there is an issue, it's a 403 issue."

Dr. Barkin began with the schedule of controlled substances, explaining the significance of the numerals and the classification of various drugs. He then discussed the Physician Desk Reference ("PDR"), which was admitted without objection. Dr. Barkin read aloud parts of the PDR pertaining to Schedules II, III, and IV, which discuss the requirements for prescriptions of specific substances and the risk of abuse. For example, he quoted the PDR as stating that the use of substances in Schedule II "may lead to severe physical or psychologic depend[e]nce. Prescriptions must be written in ink, or typewritten, signed by the practitioner. Verbal prescriptions must be confirmed in writing within 72 hours, and may be given only in a genuine emergency. No renewals are permitted."

Dr. Barkin continued by addressing the factors that physicians consider prior to prescribing controlled substances, specifically referencing the procedures followed by his employer, the Rush Pain Center. He testified about the need to meet with patients in person and to determine the correct dosage on an individual basis. He explained that dosage depends on the patient's kidney and liver function, weight, height, other medications being taken, and child-bearing potential. Dr. Barkin emphasized that this could not be done over the Internet.

Next, Dr. Barkin addressed thirteen specific drugs or types of drugs, explaining whether they are controlled substances,4 how they are scheduled, why they are prescribed, and why a prescription is needed.5 Dr. Barkin testified that Ritalin is a Schedule II controlled substance used to address Attention Deficit Disorder. He explained that use of Ritalin requires inperson monitoring and that users should not crush or snort it. He warned that use of Ritalin could result in birth defects and psychotic episodes, as well as "[d]rug depend[e]nce, abnormal thinking, and abnormal behaviors, frank psychotic episodes." In discussing Valium, Ativan, and Xanax, Dr. Barkin identified the severe risk of birth defects and the danger of seizures if a patient abruptly stops taking these substances. He testified that Rohypnol is an "extremely fast onset sedative hypnotic" that is not available in United States and that causes a user to become "completely disinhibited, helpless, very sedated" with a "complete lack of recall and memory." Dr. Barkin explained that Clenbuterol, used to treat asthma and to strengthen animals, is not a controlled substance but is nonetheless unavailable in the United States due to "tremendous risks."

Dr. Barkin described anabolic steroids in greater detail, beginning with their Schedule III classification and their use in treating testosterone deficiency, breast cancer, and prostate cancer. He cautioned that users must be monitored due to the severity of the potential side effects, which include large breasts for males, virilization in women, agitation, anger, violence, episodic discontrol, cardiac disease, increase in cholesterol, birth defects, coagulation problems, adverse effects on the liver, and stunted growth for teens. He referred to Phentermine, Didrex, and Bontril as controlled substances that are used as appetite suppressants. Dr. Barkin focused on the risks of Ambien and Halcion, both Schedule IV controlled substances that are used as sleep aids. Before prescribing Ambien, physicians counsel the patient to determine the cause of the insomnia and take into account the patient's liver function, kidney function, psychopathology, and alcohol usage. Halcion comes with side effects of birth defects and fast-onset memory impairment and judgment problems. Dr. Barkin noted that Halcion has "grown into substantial disuse" due to the severity of these side effects. Finally, Dr. Barkin described the weight-loss drug, Meridia, which requires monitoring because it can cause seizures and affects the rate, rhythm, conduction, and contractility of the heart.

During cross-examination, Dr. Barkin admitted that he does not know who the clients are or have any personal knowledge of the facts of this case.

In its closing argument, the government emphasized Dr. Barkin's testimony, connecting it to the offenses charged in the following manner:

Boros's counsel also referred to Dr. Barkin's testimony during his closing argument, saying: "[I]t just doesn't make sense to me that you would, as a prosecutor, bring some of this stuff forward, because... somebody like Dr. Barkin, who they dragged out here, he was very frank, he didn't know a single thing about this case."

On May 20, 2008, a jury returned a guilty verdict on all three conspiracy charges. The court sentenced Boros to nine years' imprisonment, followed by five years of supervised release.

II. Discussion

Boros argues that the district court erred in admitting Dr. Barkin's testimony because the testimony was not relevant. Viewing the testimony in the context of the circumstances of this case, we determine that the testimony had only minimal relevance as background evidence. While we conclude that the testimony satisfies Rule 401's low threshold for relevance, we hold that certain parts of the testimony should have been excluded under Rule 403 due to their potential for unfair prejudice. We nevertheless affirm the judgment of the district court because we conclude that the erroneous admission of Dr. Barkin's complete testimony was harmless.

A. Relevance Under Rule 401

We review a district court's decision to admit or exclude evidence for abuse of discretion. United States v. Penaloza, 648 F.3d 539, 544 (7th Cir.2011). We have recognized that a district court has "wide discretion" when it rules on the admission of evidence. United States v. Hall, 165 F.3d 1095, 1117 (7th Cir.1999) (quoting United States v. Wilson, 985 F.2d 348, 351 (7th Cir.1993)). We "will not substitute [our] opinion for that of the trial judge merely because we may be inclined to rule differently on the question of relevancy." United States v. Bouye, 688 F.2d 471, 476 (7th Cir.1982). Rule 401 defines relevant evidence as evidence having "any tendency to make a fact more or less probable than it would be without the evidence" and where "the fact is of consequence in determining the action." FED.R.EVID. 401. Rule 402 provides the corollary that, with certain exceptions, "[r]elevant evidence is admissible" and "[i]rrelevant evidence is not admissible." FED.R.EVID. 402. A party faces a significant obstacle in arguing that evidence should be barred because it is not relevant, given that the Supreme Court has stated that there is a "low threshold" for establishing that evidence is relevant. Tennard v. Dretke, 542 U.S. 274, 285, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004). We have recently asserted that "[t]he Federal Rules of Evidence do not limit the government to the `most' probative evidence; all relevant evidence is admissible and the Rules define relevance broadly." United States v. McKibbins, 656 F.3d 707, 711 (7th Cir.2011).

Boros argues that the district court abused its discretion because Dr. Barkin's testimony was not relevant. Specifically, Boros contends that the testimony did not make it any more or less likely that the conspiracy existed or that Boros knew about the conspiracy. He argues that the testimony was introduced only to frighten the jurors with evidence of the possible effects of drug use. In response, the government argues that the testimony was relevant both for background purposes and for contesting Boros's claim that he did not know that the operations were illegal.

Boros is incorrect in his assertion that evidence is only relevant if it relates to an element of the offense. Rule 401 makes clear that "[e]vidence which is essentially background in nature can scarcely be said to involve disputed matter, yet it is universally offered and admitted as an aid to understanding." FED.R.EVID. 401 advisory committee's note. Under this theory of relevance, we have explained that one measure of relevance is whether "its exclusion would leave a chronological and conceptual void in the story." United States v. Westbrook, 125 F.3d 996, 1007 (7th Cir.1997) (quoting Wilson v. Groaning, 25 F.3d 581, 584 (7th Cir.1994)) (internal quotation marks omitted). Thus, even though evidence may not relate directly to the defendant's innocence or guilt, or even to a fact in dispute, evidence is relevant when it provides background information about the defendant or the offenses charged. Certain background evidence may touch on ancillary, rather than the core, issues: evidence of this nature has marginal relevance, but it nonetheless satisfies Rule 401. Yet because background evidence about ancillary matters has only marginal relevance, it is more susceptible to exclusion under Rule 403's balancing of prejudice and probative value.

Dr. Barkin's testimony falls within the broad category of background evidence because it aids the jury's understanding of the substances that PMeds was obtaining, importing, and selling. The status of the substances as controlled relates to an element of the offenses. See 18 U.S.C. § 1956; 21 U.S.C. §§ 841, 846, 952, 963. The district court's issuance of a jury instruction on this matter confirms the relevance of this topic. The remainder of the testimony—the prescribed uses, the degree of physician monitoring, the accessibility, and the side effects—are arguably relevant for the purpose of providing a complete background picture to the jury.6 Whether this ancillary background evidence is unduly prejudicial—and thus should have been excluded—is not a question that we consider under Rule 401 but rather under Rule 403.7

We therefore conclude that the district court did not abuse its discretion in determining Dr. Barkin's testimony to be relevant. However, even accepting Dr. Barkin's testimony as satisfying Rule 401, we conclude that parts of his testimony do not satisfy Rule 403 and thus should have been excluded.

B. Prejudice Under Rule 403

Rule 403 permits a district court to "exclude relevant evidence if its probative value is substantially outweighed by a danger of . . . unfair prejudice, confusing the issues, misleading the jury, undue delay, wasting of time, or needlessly presenting cumulative evidence." FED.R.EVID. 403. Recognizing that "`most relevant evidence is, by its very nature, prejudicial,' we have emphasized that evidence must be unfairly prejudicial to require exclusion." United States v. Hanna, 630 F.3d 505, 511 (7th Cir.2010) (quoting United States v. Thomas, 321 F.3d 627, 630 (7th Cir.2003)). The amount of prejudice that is acceptable varies according to the amount of probative value the evidence possesses. "[T]he more probative the evidence, the more the court will tolerate some risk of prejudice, while less probative evidence will be received only if the risk of prejudice is more remote." United States v. Vargas, 552 F.3d 550, 557 (7th Cir.2008) (quoting United States v. Menzer, 29 F.3d 1223, 1234 (7th Cir.1994)). We give "special deference" to a district court's findings under Rule 403, and we review for abuse of discretion. See United States v. Moore, 641 F.3d 812, 826 (7th Cir.2011).

The district court made several comments, which indicated that it was aware of the prejudice that could result from Dr. Barkin's testimony. The district court warned, "I don't want this to get out of control and have him testifying about the terrible things that can happen to people if they take these drugs without a prescription, except indicating it factually, and briefly, and succinctly." But given the limited probative value of this testimony, the court erred by allowing even factual, brief, and succinct testimony about the side effects and birth defects associated with the drugs.

The mere acknowledgment that Dr. Barkin's testimony was relevant under Rule 401 as background evidence does not signify that all of the testimony passed muster under Rule 403. When background evidence is so removed from the focus of the case, as it was here, even factual, brief, and succinct testimony may be unfairly prejudicial to the defendant. We have stated that both probative value and prejudice must be determined in context. See United States v. Tanner, 628 F.3d 890, 901-03 (7th Cir.2010) (holding police officers' testimony to be "unduly prejudicial (and such a waste of time) relative to its nearly-nonexistent probative value"). The district court does not appear to have focused on this interaction.

Dr. Barkin's testimony was relevant because it constituted background evidence about the regulatory scheme and the dangers that could result from PMeds's illegal operation. However, this background evidence bore minimal probative value given the particular offenses with which Boros was charged. The jury was asked to determine whether Boros was guilty of conspiracy to import controlled substances, conspiracy to possess controlled substances with intent to distribute, and conspiracy to launder money.8 These offenses do not require the government to prove that Boros was aware of the regulatory scheme or the medical risks. These offenses also do not require proof that anyone was injured as a result of Boros's or his co-conspirators' conduct. In United States v. Mansoori, 304 F.3d 635, 654 (7th Cir.2002), we held that expert testimony about the history and structure of a gang was admissible as "useful background" and was not unfairly prejudicial or confusing. We do not reach the same conclusion as to Dr. Barkin's testimony about the drugs' side effects, which was less useful and more prejudicial.

We have previously held that evidence showing that defendant's customers died after buying drugs from him should have been excluded under Rule 403 because the evidence "had nothing to do with the charges in th[e] case." United States v. Cooper, 591 F.3d 582, 589 (7th Cir.2010). Dr. Barkin's testimony is less prejudicial than the testimony in Cooper because it does not directly connect the side effects to Boros's customers; however, this disconnect also confers less probative value on Dr. Barkin's testimony.

While Dr. Barkin kept his testimony relatively brief and though his tone was academic rather than emotional, parts of the content could be described as disturbing. Dr. Barkin discussed side effects such as seizures, strokes, psychotic episodes, and birth defects. Dr. Barkin's disclaimer that he did not know any of PMeds's clients or their side effects does not mitigate his discussion of the negative consequences that could stem from the use of the drugs.

Evidence bearing minimal probative value is admissible only if it bears a remote risk of prejudice. See Vargas, 552 F.3d at 557. Dr. Barkin's testimony about the drugs' side effects and birth defects had a meaningful potential for unfair prejudice, which substantially outweighed the limited probative value of the background evidence. We therefore conclude that the district court abused its discretion in admitting these parts of the testimony.

C. Harmless Error Analysis

Even though we conclude that the district court erroneously admitted Dr. Barkin's complete testimony, we will "reverse and order a new trial only if any evidentiary errors are not harmless." United States v. Boone, 628 F.3d 927, 932 (7th Cir.2010); see also FED.R.CRIM.P. 52(a) ("Any error, defect, irregularity, or variance that does not affect substantial rights must be disregarded."). In determining whether the error is harmless, "we consider whether, in the mind of the average juror, the prosecution's case would have been significantly less persuasive had the improper evidence been excluded." United States v. Thornton, 642 F.3d 599, 605 (7th Cir.2011); see also United States v. Johnson, 624 F.3d 815, 819 (7th Cir. 2010). To determine whether an error is harmless, we consider the entirety of the evidence that the government presented. See McKibbins, 656 F.3d at 713. Evidence erroneously admitted under Rule 403 warrants reversal only if its exclusion would have made the jury more likely to acquit the defendant. See Tanner, 628 F.3d at 902-03. Given the evidence presented in support of his convictions, Boros has not established that the government's case would have been significantly less persuasive to the jury had Dr. Barkin's improper testimony been excluded.

The government established Boros's guilt through various pieces of documentary evidence and insider testimony. The letter of intent identified Boros's role in PMeds. Boros advertised that PMeds would supply prescription drugs without prescriptions. Boros sent emails describing the drug supply, suggesting a supplier, and providing a "usage report" of 235 products, including controlled substances, by quantity. Moreover, Boros said nothing to express his surprise or disclaim his participation when the Calows referenced their illegal actions over email. Boros responded to an email chain about website traffic by stating that he was "ready to do a mailing anytime you want." He expressed no shock or disapproval when Gary admitted to instructing a "young kid" on how to order an injectable anabolic steroid. When Larry boasted that PMeds was "doing great [with] the illegal drugs" and that he also wanted to have "one legal Pharmacy," Boros again did not express concern but instead replied that they should "get together" to "make a plan."

Burdick's testimony also supports Boros's conviction. Based on her employment at PMeds, which overlapped with Boros's involvement, she explained how PMeds operated and identified the roles of the founders. Despite Boros's claim that Burdick's testimony is uncorroborated, the search of the Tinley Park office, the evidence related to the controlled buys, the letter of intent, and the email exchanges all support her testimony.

The testimony from Morrow and Special Agent Desmond also support the jury's verdict. Morrow testified about the general nature of the PMeds scheme as designed to import and distribute anabolic steroids and controlled substances. His testimony was corroborated by other evidence, including the email exchanges and his own arrest in 2005 at the border. Special Agent Desmond testified about the financial operations, including how PMeds wired money to suppliers in Belize and to people affiliated with PMeds in Mexico. By Boros's own admission, he received approximately $47,000 for his participation in PMeds.

The only argument that Boros advances on appeal to refute the government's case is the testimony from a credit card processing employee, who stated that Boros had told him to "cut them off" after Boros allegedly discovered PMeds's illegality. This scant testimony does not counter the amount of evidence introduced by the government that establishes Boros's guilt.9

Dr. Barkin's testimony had minimal relevance, minimal probative value, and overtones of prejudice. If the evidence as to Boros's guilt had been less compelling, the government's use of the testimony relating to the consequences of drug use might have impacted the outcome of this case. However, in light of the evidence in support of Boros's guilt, excluding Dr. Barkin's testimony would not have led an "average juror" to find that the evidence was "significantly less persuasive." Cooper, 591 F.3d at 590. Thus, though we conclude that the district court should have excluded parts of Dr. Barkin's testimony, we determine that the evidentiary error was harmless.

III. Conclusion

For the foregoing reasons, we AFFIRM the judgment of the district court.