GORSUCH, Circuit Judge.

When calculating an advisory guidelines sentence for an economic crime a district court naturally must take account of the losses the defendant caused others. But the guidelines instruct that, when fashioning a sentence, a court should also account for the losses the defendant "intended" but was unable to realize. The question we face in this case is what counts as an "intended" loss? Unsurprisingly, we hold that the term means exactly what it says: to be included in an advisory guidelines calculation the intended loss must have been an object of the defendant's purpose.

Afuhia Masiu Manatau was in the business of stealing identities. But while he had the benefit of much practice, he was no more successful for it. Over the course of a year he stole buckets of social security numbers, credit cards, and checks. But he was also caught by police in the act no fewer than five times before the federal government finally indicted him. Two of these encounters illustrate the nature of Mr. Manatau's scheme. Once, the police stopped Mr. Manatau's car and found him with two stolen "convenience checks." These convenience checks, issued by a credit card company, allow a credit card holder to write a check against his or her line of credit, with the amount of any check written charged to the cardholder's account. Mr. Manatau also had in his possession a credit card statement revealing that the credit limit on the stolen checks exceeded $30,000. On another occasion, the facts were similar but different. A victim reported two credit card convenience checks stolen in a car burglary. The credit limit on these checks exceeded $10,000, but there is no indication that Mr. Manatau ever saw a statement reflecting that fact or that he had any idea the checks were good for that much. We do know, however, that by the time the authorities caught up with him this time he had already cashed both checks on this account for just over $1,800 and had no other checks left.

Shortly after his indictment and recognizing the weight of the evidence against him, Mr. Manatau pleaded guilty to bank fraud and aggravated identity theft. See 18 U.S.C. § 1344; 18 U.S.C. § 1028A. The case then turned to the question of an appropriate sentence. Seeking to calculate the applicable advisory guidelines sentence, the district court focused on U.S.S.G. § 2B1.1(b)(1). Under that provision, a court must compare the economic loss the defendant "actual[ly]" inflicted on his victims with the loss he "intended to result from the offense" even if it was never realized. See U.S.S.G. § 2B1.1 cmt. n. 3(A)(i)-(ii). A court must identify the greater figure, the actual or intended loss, and then proceed to one of the guidelines' inevitable charts. Relevant for our purposes, the chart in § 2B1.1 indicates that if the greater of the actual or intended loss figure falls between $10,000 and $30,000 the defendant's offense level should be increased four levels. At the same time, the chart suggests that if the greater loss figure is more than $30,000 but less than $70,000, the defendant's offense level should be increased six levels. The difference between a four- and six-level offense ultimately translates into a different recommended prison sentence. In this case, a difference of approximately six to twelve months.

And it is this difference that is the focus of our dispute. There's no question that the actual loss Mr. Manatau inflicted on his victims was only about $1,840. But there's a very live question about what additional but unrealized loss he may have intended.

Before the district court, the government argued that Mr. Manatau's "intended loss" was more than $60,000 and so merited a six level offense increase. To reach this figure, the government argued (among other things) that the district court should simply tote up the credit limits of the stolen convenience checks. Whether or not Mr. Manatau ever intended to reach those credit limits, the government said, is neither here nor there. It is enough, the government represented, that a loss up to the credit limits was "both possible and potentially contemplated by the defendant's scheme." Aplt.App. Vol. 1 at 72 (emphasis added); see also Aple. Br. at 23.

To this, Mr. Manatau objected. He conceded that his intended loss was significantly higher than the $1,800 actual loss he caused. But he argued that the government's intended loss analysis rested on a legal error. He said an inquiry into a defendant's mens rea is required when determining his "intended loss." And that such an inquiry in his case would show that he didn't intend to reach the available credit limits on at least some of the convenience checks. For example, with respect to the second incident discussed above, Mr. Manatau argued that he could not possibly have intended a loss up to the full credit limit of $10,000. He couldn't have, he said, because he never saw a statement indicating that the credit limit was so high; he had no other way to know the limit would be so high; he stole only two convenience checks; by the time the police caught him he had already negotiated both of them for approximately $1,800; and he had no means to write any further checks on the account. Given these facts, he said, his intended loss for this transaction should be calculated at about $1,800, not $10,000. And a comprehensive analysis of all five transactions would show that his intended loss was somewhere between $10,000 and $30,000 and so justify only a four level offense increase, not the six level increase proposed by the government.

Ultimately, the district court overruled Mr. Manatau's objections. It employed the six level increase proposed by the government and imposed a within-guidelines sentence of 42 months, followed by 60 months of supervised release. Now on appeal, Mr. Manatau renews his argument that the district court failed as a matter of law to apply the proper mens rea standard when calculating his "intended loss."

We agree. We hold that "intended loss" means a loss the defendant purposely sought to inflict. "Intended loss" does not mean a loss that the defendant merely knew would result from his scheme or a loss he might have possibly and potentially contemplated. Several factors compel our conclusion.

First, the plain language. The guidelines define the term "intended loss" as the "pecuniary harm that was intended to result from the offense," including "intended pecuniary harm that would have been impossible or unlikely to occur." U.S.S.G. § 2B1.1 cmt. n. 3(A)(ii) (emphasis added). This definition is, of course, seriously circular, using the term "intended" to define itself not just once but twice. At the same time, the sentencing commission's definition offers us no reason to think it wished us to apply anything other than the word's ordinary meaning. If anything, the commission's (repeated) use of the word "intended" to define itself suggests that the commission thought the word's meaning was pretty plain. And in contemporary usage, it is. Something is intended if it is done on purpose—not merely known, foreseen, or just possible or potentially contemplated. 7 Oxford English Dictionary 1074 (2d ed. 1989); Webster's Ninth New Collegiate Dictionary 629 (1985) (defining "intend" as "to have in mind as a purpose or goal"). "That knowledge [alone] is sufficient to show intent is emphatically not the modern view." Giles v. California, 554 U.S. 353, 368, 128 S.Ct. 2678, 171 L.Ed.2d 488 (2008); see also Wayne R. LaFave, Substantive Criminal Law § 5.2(b) at 343 (2d ed. 2003).

The Model Penal Code reflects this contemporary understanding. Taking pains to distinguish intent from knowledge, the Code states that a person acts "intentionally" if he acts "purposely" or had as a "conscious object" to cause a particular result. Model Penal Code ("MPC") § 1.13 (1985); MPC § 2.02(2)(a)(i). By contrast, a person acts "knowingly" if "he is aware that it is practically certain" his conduct will cause a result. MPC § 2.02(2)(b)(ii); see also United States v. Lopez-DeLeon, 513 F.3d 472, 474 (5th Cir.2008) (reviewing the Model Penal Code to discern the "ordinary, contemporary, [and] common meaning" of a term used in the guidelines); United States v. Borer, 412 F.3d 987, 992 (8th Cir.2005) (same); United States v. Honeycutt, 8 F.3d 785, 787 (11th Cir.1993) (same).

The difference between these two mental states—between intent and knowledge— is, put simply, the difference "between a man who wills that a particular act or result take place [intent] and another who is merely willing that it should take place [knowledge]." MPC § 2.02 cmt. 2 at 233 n. 6 (quoting 1 Brown Comm'n Working Papers 124). It is the difference between a utility that provides telephone service to a customer "knowing it is used for bookmaking" and someone else who strings a telephone wire in order to set up the bookmaking operation; the difference between a "farm boy [who] clears the ground for setting up a still, knowing that the venture is illicit" but just looking for a paying day's work, and someone who clears the ground in order to work a still. MPC § 2.06 cmt. 6(c) at 316. Of course, lawmakers are free and sometimes do choose to mete out the same punishment for criminal wrongs whether committed intentionally or knowingly. But it is equally true that American criminal law often restricts liability to (or imposes heightened liability in) cases where an intentional choice to do a wrong is present. As Justice Jackson explained, "[t]he contention that an injury can amount to a crime only when inflicted by intention is no provincial or transient notion. It is as universal and persistent in mature systems of law as belief in freedom of the human will and a consequent ability and duty of the normal individual to choose between good and evil." Morissette v. United States, 342 U.S. 246, 250, 72 S.Ct. 240, 96 L.Ed. 288 (1952); see also Tison v. Arizona, 481 U.S. 137, 150, 107 S.Ct. 1676, 95 L.Ed.2d 127 (1987). And modern American criminal law is replete with examples—ranging from homicide law (where the availability of the death penalty or the degree of culpability sometimes depends on the question of intent) to treason, complicity, conspiracy, and attempt law (where liability is often restricted solely to cases where intent is present). The simple fact is intent and knowledge are different things, different as a matter of their plain meaning, different in their treatment in modern American criminal law. And the sentencing commission chose here to invoke the former term, not the latter.

Second, context confirms the point. The guidelines' definition of "intended loss" makes no mention of knowledge or some lesser mens rea standard. Yet, just a few lines later, the sentencing commission's definition of "actual loss" does just that— defining "actual loss" to include the "harm that the defendant knew . . . was a potential result of the offense." U.S.S.G. § 2B1.1 cmt. n. 3(A)(iv) (emphasis added). This contextual clue signals that the commission both understood the difference between intent and knowledge and used those terms in their distinct, ordinary, and modern senses. It shows, too, that if the commission had wished to include the "knowledge" concept in the definition of intended loss it well knew how to do so.

Still another portion of § 2B1.1 suggests the same conclusion. That portion recommends a particular enhancement "[i]f the offense involved misappropriation of a trade secret and the defendant knew or intended that the offense would benefit a foreign government. . . ." U.S.S.G. § 2B1.1(5) (emphasis added). So here again the commission distinguished between intent and knowledge, indicating its appreciation of the difference between the two concepts; in fact, its reference to "knew or intended" would be superfluous by half if the commission understood the term "intent" to capture knowledge already. See Hibbs v. Winn, 542 U.S. 88, 101, 124 S.Ct. 2276, 159 L.Ed.2d 172 (2004) ("A statute should be construed so that effect is given to all its provisions, so that no part will be inoperative or superfluous, void or insignificant." (internal quotation omitted)). At the same time, this particular portion of § 2B1.1 demonstrates that the commission is able and willing to decide when a particular sentencing enhancement should not turn on the distinction between intent and knowledge. And the fact that the commission chose in the very same guidelines section to authorize identical punishment for a knowing or intended misappropriation of a trade secret cannot help but suggest that it acted deliberately when it did not do the same thing when defining "intended loss." See Russello v. United States, 464 U.S. 16, 23, 104 S.Ct. 296, 78 L.Ed.2d 17 (1983) ("Where Congress includes particular language in one section of a statute but omits it in another section of the same Act, it is generally presumed that Congress acts intentionally and purposely in the disparate inclusion or exclusion." (internal quotation omitted)).

Third, looking beyond the confines of § 2B1.1 reinforces all these points. A guidelines provision related to "property damage or loss" authorizes a court to enhance a sentence based "on the extent to which the harm was intended or knowingly risked." U.S.S.G. § 5K2.5 (emphasis added). Many other provisions likewise bracket intended and knowing conduct for similar treatment. See, e.g., U.S.S.G. § 5K2.1 ("intended or knowingly risked"); § 5K2.2 (same); § 5K2.3 (same); § 8C4.2 (same); § 1A1.4(f) ("knowledge or intent"); § 2K2.1(c) (same); § 2K2.5(c) (same); § 2K1.3(b)(3) ("knowledge, intent, or reason to believe"); § 2K2.1(b)(6) (same); § 2M5.3(b) ("intent, knowledge, or reason to believe"); § 2M5.3 cmt. ("known or intended"); § 2X3.1 cmt. (same). All these provisions again stand in sharp contrast to the definition of "intended loss," which makes no mention of a knowledge standard. And all would be a nonsense if the term "intent" already encompassed "knowledge."

Fourth, our interpretation fits with background legal norms. In the "law of inchoate offenses such as attempt and conspiracy" a showing of intent is often what "separates criminality itself from" what the law treats as purely "innocuous behavior." United States v. Bailey, 444 U.S. 394, 405, 100 S.Ct. 624, 62 L.Ed.2d 575 (1980); see also LaFave, Substantive Criminal Law § 5.2(b) at 342-43 & n. 9; MPC § 2.02 cmt. 2 at 234. This even though a lesser mens rea showing may suffice to establish liability for the same completed offense. See, e.g., Braxton v. United States, 500 U.S. 344, 351 n. *, 111 S.Ct. 1854, 114 L.Ed.2d 385 (1991); Bailey, 444 U.S. at 404-05, 100 S.Ct. 624; LaFave, Substantive Criminal Law § 11.3 at 211-12; MPC § 5.01 cmt. 2 at 301; Joel Prentiss Bishop, New Commentaries on the Criminal Law § 729.4 (8th ed. 1892). A similar phenomenon runs through the law of accessory liability. While criminal liability may attach to the primary criminal offenders on a lesser mens rea showing, proof of intent is often required to hold liable those only tangentially involved with the illegal enterprise. See MPC § 2.02 cmt. 2 at 234; MPC § 2.06 cmt. 6(c) at 313-19. Of course (and again), legislators are free to vary these rules and sometimes they have, but the traditional American dichotomy between the mens rea treatment of completed and incompleted offenses, and between principal and accessory liability, is no doubt a product of "an intense individualism . . . root[ed] in American soil" willing to attach criminal sanction for actions indirectly (or not at all) responsible for harm befalling others only if a deliberate choice to do wrong is present. Morissette, 342 U.S. at 251-52, 72 S.Ct. 240; United States v. Gracidas-Ulibarry, 231 F.3d 1188, 1193 (9th Cir. 2000) ("When the defendant's conduct does not constitute a completed criminal act,. . . a heightened intent requirement is necessary to ensure that the conduct is truly culpable."); United States v. Falcone, 109 F.2d 579, 581 (2d Cir.1940) (Learned Hand, J.) (proof of criminal intent is required to prevent a "drag-net of conspiracy" from sweeping up innocent conduct). And it is hardly surprising that the sentencing commission might wish to mimic in sentencing law what has long held true in substantive American criminal law by allowing liability for losses that have actually accrued to real victims on a lesser mens rea showing, while requiring the government to meet a higher mens rea showing of intent before imposing liability for unrealized or inchoate losses.1

Fifth, the government's alternative definition of "intended loss" is implausible on its face. While the government sometimes seems to ask us to conflate intent with knowledge, other times it urges us to be bolder still, urging us to define "intended loss" as any loss that was "possible and potentially contemplated by [the] defendant's scheme." Aple. Br. at 23 (emphasis added). And this, of course, is exactly the tack the government (successfully) took before the district court. But whatever the term "intent" might mean, we have never heard of a definition that would allow us to say that an individual's intentions include things he never contemplated—except perhaps in an Opposite Day game.

The government's alternative definition is untenable for still other reasons. The government says, for example, an intended loss must be a possible loss. Yet the guidelines expressly define intended loss to "include[ ] intended pecuniary harm that would have been impossible or unlikely to occur." U.S.S.G. § 2B1.1 cmt. n. 3(A)(ii) (emphasis added). It is passing strange that the government would wish to limit liability for intended losses to those that are possible in the face of language in the guidelines expressly indicating that intended losses need not be possible.

The government's definition would also render the guidelines' "actual loss" provision surplusage. Section 2B1.1 defines "actual loss" as the "reasonably foreseeable pecuniary harm that resulted from the offense." U.S.S.G. § 2B1.1 cmt. n. 3(A)(i) (emphasis added). But if, as the government urges, the term "intended loss" simply means a loss that is "possible and potentially contemplated"—a formulation that seems no different than "reasonably foreseeable" harm that resulted or might have resulted from the offense— then a defendant's "intended loss" would always be at least his "actual loss." And if intended loss were always greater than or equal to actual loss, the guidelines could have simply instructed the courts to calculate intended loss. Actual loss would be irrelevant—and surely that can't be a plausible result. See Hibbs, 542 U.S. at 101, 124 S.Ct. 2276.

Sixth, our precedent does much to support and nothing to preclude our holding. The government cites United States v. Lin in an effort to suggest that no mens rea is required when proving intended losses. 410 F.3d 1187, 1190 (10th Cir.2005). But in that case, it turns out, we affirmed an "intended loss" figure based on a district court's factual finding that the defendants subjectively intended the loss in question. Id. at 1190. The government rejoins that we described the intended loss in Lin as the full credit limit of the stolen credit cards. But we did so in Lin only because there the government proved and the district court found that the defendants "intended to . . . test the limits of the [credit] cards" they possessed. Id. (emphasis added). In this case, of course, the government has, so far at least, attempted to make no similar factual showing about the defendant's mens rea and it has even sought to disclaim the need to do so.2

Some four years after Lin, moreover, we observed in United States v. Baum that the question of what particular level of mens rea § 2B1.1 requires remained an open one in this circuit. See 555 F.3d 1129, 1135 (10th Cir.2009). We acknowledged that some of our decisions could be read to suggest that something less than intent or purpose might suffice. But we explained that these earlier discussions were dicta because in each case "there was clear evidence that the defendant realistically intended" the loss in question, so any discussion of a lower mens rea standard was inessential to our decision. See id. at 1134 (internal quotation omitted); N.L.R.B. v. Int'l Brotherhood of Elec. Workers, 481 U.S. 573, 591 n. 15, 107 S.Ct. 2002, 95 L.Ed.2d 557 (1987) (statements "unnecessary to the disposition of" a case are dicta). We also stressed that the dicta in our earlier cases was itself questionable in light of subsequent developments. We noted that all of our cases suggesting a lower mens rea standard "trace[d] back to" United States v. Smith, 951 F.2d 1164 (10th Cir.1991). See Baum, 555 F.3d at 1134. And in Smith we relied on an application note to a guidelines provision that included the concept of "probable" losses that the government now advocates. See 951 F.2d at 1168. But, we pointed out in Baum, reliance on that note may no longer be possible because it was amended long ago to delete reference to "probable" losses. See 555 F.3d at 1135. So it is that, as Baum observed, our precedent to date has always applied an intent standard even while sometimes (mistakenly) giving lip service in dicta to a lower mens rea standard.3

Neither has the government identified any extra-circuit authority inconsistent with our decision. Just as we do, the Fifth Circuit requires "the government [to] prove by a preponderance of the evidence that the defendant had a subjective intent to cause the loss." United States v. Sanders, 343 F.3d 511, 527 (5th Cir.2003); see also United States v. Wells, 127 F.3d 739, 746 (8th Cir.1997). For its part, the government fails to cite Sanders or Wells and instead draws our attention to United States v. Mei, 315 F.3d 788 (7th Cir.2003). But, much like our precedent, any suggestion about a possibly lower mens rea standard in Mei is no more than dicta. Fact is, the Seventh Circuit in Mei ruled that the intended loss figures before it can "hold water only if, as the district court found, Mei intended to gouge his victims for every penny he could with every [credit] card that he had in every way that he knew." 315 F.3d at 793. And the Seventh Circuit proceeded to rest its holding on the ground that there was indeed "plenty of evidence . . . to conclude that Mei intended" to cause the losses in question. Id. The First Circuit's decision in United States v. McCoy is likewise consistent with our decision. There, the court held that "intended loss" can be shown by looking to what loss was "expected" because under its circuit precedent a person is presumed to have "intended the natural and probable consequences of his or her actions." McCoy, 508 F.3d 74, 79 & n. 6 (1st Cir. 2007) (internal quotation omitted). And with this we hardly disagree. Juries and judges can and often must reach conclusions about a defendant's mens rea based on inferences from known facts about his conduct. Few, after all, will admit to harboring an unlawful mens rea. But just because a factfinder may infer something about a defendant's mens rea from his actions does not mean the government is liberated from proving that mens rea. Conflating these two points would be a fallacy indeed. See LaFave, Substantive Criminal Law § 5.2(f) at 355-58 ("[W]hat [a defendant] does and what foreseeably results from his deeds have a bearing on what he may have had in his mind."); Bishop, New Commentaries on the Criminal Law § 734.1.

Seventh, though we see no ambiguity in the term "intended loss," if there were any that would only provide another reason for the same result. After all, the rule of lenity teaches that if, after "seizing every thing from which aid can be derived" an ambiguity still persists, Smith v. United States, 508 U.S. 223, 240, 113 S.Ct. 2050, 124 L.Ed.2d 138 (1993) (internal alteration and quotation omitted), courts should interpret federal criminal statutes—including, we have said, the sentencing guidelines—"to avoid an increase in the penalty prescribed for the offense," United States v. Hinckley, 550 F.3d 926, 932 n. 4 (10th Cir.2008); United States v. Weidner, 437 F.3d 1023, 1046-47 (10th Cir. 2006); United States v. Bazile, 209 F.3d 1205, 1207 (10th Cir.2000); see also United States v. R.L.C., 503 U.S. 291, 305-06, 112 S.Ct. 1329, 117 L.Ed.2d 559 (1992). And that principle plainly would support treating intent to mean purpose rather than some lower standard likely to increase the defendant's sentence.

In the end, then, we hold that the mens rea standard for "intended losses" is just what the plain language and structure of the guidelines suggest—requiring an inquiry into the defendant's purpose. And given this, it is clear the district court committed legal error. At the government's urging, the district court declined to make any effort to determine whether Mr. Manatau intended (had the purpose) to cause the losses in question.

Neither can we be sure this error was harmless. See Fed.R.Crim.P. 52(a). The district court imposed a within-guidelines sentence and appeared to give the advisory guidelines much weight in its own ultimate sentencing decision. But when calculating the suggested guidelines sentence range, the court imposed a six level enhancement for Mr. Manatau's intended losses—rather than the four level enhancement he conceded was appropriate—based on an erroneous legal standard for assessing intended loss. And we simply can't be certain whether the threshold for a six level enhancement is or isn't met under the correct legal standard. By way of example, take the incident where Mr. Manatau was caught after stealing and cashing two convenience checks for $1,800. The district court attributed $10,000 in intended loss to Mr. Manatau based on the available credit limit, reasoning that it was possible that he could have imposed that much loss. But as adduced so far the facts in the record suggest that Mr. Manatau had no idea what the available credit limit was; that he possessed and cashed just two checks for a total of about $1,800; and that he had no means for accessing the remainder of the credit limit. On this record at least, it is unclear how Mr. Manatau could have intended to steal (that is, had the purpose of stealing) six times more than the amount actually stolen when he no longer had any checks left to cash.

None of this is to say Mr. Manatau will succeed in persuading the district court that only a four level enhancement is proper. Let alone that the district court is bound by the guidelines' recommendations about the appropriate sentence. It is to say only that we cannot rule out the possibility that a correctly calculated guidelines range could yield a different advisory sentence—or that a different advisory sentence could yield a different final sentence from the district court. And that is enough to preclude a finding of harmless error and warrant a remand. See United States v. Todd, 515 F.3d 1128, 1134-35 (10th Cir.2008) ("When a district court does err in calculating the applicable Guidelines range, we must remand for resentencing. . . unless we are able to ascertain that the court's calculation was harmless" because "the starting point and the initial benchmark for any sentencing decision must be a correctly calculated Guidelines sentencing range." (internal quotation omitted)).

On remand, the district court should examine what losses Mr. Manatau intended. Of course, in answering this question the court is free, as we have explained, to make reasonable inferences about the defendant's mental state from the available facts. In the sentencing context, too, the government need only prove Mr. Manatau's intent by a preponderance of the evidence, and the court need only make a "reasonable estimate" of the intended loss. See United States v. Galloway, 509 F.3d 1246, 1252 (10th Cir.2007); U.S.S.G. § 2B1.1 cmt. n. 3(C). The available credit limits on the convenience checks in question and the defendant's knowledge (or lack of knowledge) of them may well be relevant evidence bearing on what loss a defendant did (or didn't) intend. But a court cannot simply calculate "intended loss" by toting up credit limits without any finding that the defendant intended to inflict a loss reasonably approaching those limits. Once the district court has properly determined the scope of Mr. Manatau's intended loss, it must of course compare that amount to the actual loss he caused and use the greater of the two when calculating the applicable sentencing enhancement. See U.S.S.G. § 2B1.1 cmt. n. 3(A). At that point, it will have an accurately calculated advisory guidelines sentence on which to base its own sentencing decision.4

The sentence is vacated and this matter is remanded for further proceedings consistent with this opinion. Mr. Manatau's motion to supplement the record is granted.