EASTERBROOK, Circuit Judge.
A former Chicago police officer collected disability benefits while working full time. For more than two years he mailed monthly affidavits representing that he had not “resume[d] employment for compensation while in receipt of disability benefit”. One who “resumes” employment (in the language of the affidavit) or “assumes” employment (in the language of the state statute, Ill.Rev.Stat. ch. 108½, § 5-157) has his disability benefits reduced one dollar for every dollar of earnings, once the combination of disability benefits and earnings exceeds the officer’s former salary.
DeCastris had not exactly “assumed” or “resumed” employment, however. For five years before he left the police force, he had held a full-time job managing the nationwide trucking operation for Zenith Electronics Corp. The job with Zenith paid more than the job with the police. Holding two full-time jobs is forbidden by Zenith. Zenith learned of the police job in 1978 and demanded that DeCastris quit one or the other. DeCastris left the police job with disability benefits, which led to this case. The police did not learn of the Zenith job until DeCastris had collected benefits for 27 months, the maximum to which an officer with DeCastris’s nine years of service is entitled. Had he disclosed that he was making more than $2,500 a month from Zenith (which he was in 1979), disability officials testified, he would not have received disability benefits.1 The crime is mail fraud, in violation of 18 U.S.C. § 1341 [263]*263(the affidavits went by mail); the sentence is two years’ imprisonment, five years’ probation, and a fine of $5,000.
DeCastris concedes that he was working full time at Zenith and that he did not reveal this employment to the officials administering the disability program.2 He insists that this is not mail fraud because both the state statute and the monthly affidavit are ambiguous. He says that an ordinary person would think that “assume” employment means “take a new job” and that “resume” employment means “go back to your old job” — neither of which he did, because he worked at Zenith without interruption. This is not a claim that De-Castris complied with state law. The head of the disability board testified that he did not, and in the district court DeCastris argued insufficiency of the evidence rather than legal error. The prosecutor’s argument is that DeCastris intentionally put the disability board off the scent, forestalling any resolution of ambiguities in the state’s law. DeCastris’s position is that state law and the affidavit were so opaque that De-Castris should not be held criminally liable for failing to alert the board to his employment.
The crime of mail fraud is a fraudulent “scheme” facilitated by use of the mails. United States v. Lindsey, 736 F.2d 433, 436 (7th Cir.1984); United States v. Feldman, 711 F.2d 758, 765 (7th Cir.), cert. denied, 464 U.S. 939,104 S.Ct. 352, 78 L.Ed.2d 317 (1983). The mailings may be innocent or even legally necessary. United States v. Green, 786 F.2d 247 (7th Cir. 1986). Here the mailings facilitated the scheme, if there was a scheme. The question whether DeCastris practiced a scheme to extract benefits to which he was not entitled is one of fact, depending on the state of his knowledge. Concealing information known to be pertinent to a proper decision may be a fraudulent scheme. Feldman; United States v. Bush, 522 F.2d 641, 646 (7th Cir.1975); United States v. Keane, 522 F.2d 534, 544 (7th Cir.1975), cert. denied, 424 U.S. 976, 96 S.Ct. 1481, 47 L.Ed.2d 746 (1976). It is a crime to lie about your income to tax officials even if you might be able to show that you owe no tax; the parallel here is that it may be mail fraud to lie about your income to disability officials and forestall any inquiry into the effect of a second job. If DeCastris knew that he had to disclose his employment, that his earnings may have mattered no matter when he started working at Zenith, then there was a scheme to defraud, and if not, not.
The instructions presented this question squarely for the jury’s decision. They told the jurors that in order to convict DeCastris they had to be convinced that he acted “knowingly and with the intent to defraud.” Another instruction elaborated, stating that knowledge means that “the [264]*264acts charged were done knowingly and with the intent to mislead the Policeman’s Annuity and Pension Board as to the defendant’s employment at Zenith Electronics Corporation, in order to cause a financial gain to defendant. Good faith is a complete defense to the charge of mail fraud.” DeCastris did not object to this instruction. The evidence, now taken in the light most favorable to the prosecution, supports an affirmative answer. DeCastris had received a letter from the disability officials stating: “in the event disability benefit payments and regular employment compensation exceed Civil Service salary, a reduction in payment of disability benefits shall be made the following month.” This letter, coupled with the evident purport of an affidavit seeking information about employment, could lead a reasonable juror to conclude that DeCastris — a police officer, the supervisor of 90 employees at Zenith, and therefore aware of the nature of bureaucratic forms in general — knew that he had to reveal information about all earnings from employment. Cf. Screws v. United States, 325 U.S. 91, 101-07, 65 S.Ct. 1031, 1035-38, 89 L.Ed. 1495 (1945).
The prosecutor bolstered the inference by showing that DeCastris lied in response to clear questions as well as cloudy ones. The judge allowed the prosecutor to introduce ten documents containing lies. One was DeCastris’s application for employment at Zenith, which claimed more education than DeCastris possessed and omitted information about his job as a police officer. DeCastris claimed to be self-employed. Most of the rest were annual questionnaires filed with the police claiming nonexistent educational credentials. The judge excluded from evidence another form in which DeCastris told the police department that he lived in Chicago (which is legally required of a Chicago police officer); DeCastris did not live in Chicago, and the judge thought this particular lie would be unduly prejudicial. See Fed.R.Evid. 403.
DeCastris’s counsel put his intent in issue by emphasizing the ambiguity of “assume” and “resume”. (DeCastris did not testify, so we do not have his own account of his mental state.) Fed.R.Evid. 404(b) allows the introduction of “other wrong” evidence to show intent, although not to show the defendant’s character. “Intent” and “character” may merge in a case such as this, however, making the application of the rule difficult.
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EASTERBROOK, Circuit Judge.
A former Chicago police officer collected disability benefits while working full time. For more than two years he mailed monthly affidavits representing that he had not “resume[d] employment for compensation while in receipt of disability benefit”. One who “resumes” employment (in the language of the affidavit) or “assumes” employment (in the language of the state statute, Ill.Rev.Stat. ch. 108½, § 5-157) has his disability benefits reduced one dollar for every dollar of earnings, once the combination of disability benefits and earnings exceeds the officer’s former salary.
DeCastris had not exactly “assumed” or “resumed” employment, however. For five years before he left the police force, he had held a full-time job managing the nationwide trucking operation for Zenith Electronics Corp. The job with Zenith paid more than the job with the police. Holding two full-time jobs is forbidden by Zenith. Zenith learned of the police job in 1978 and demanded that DeCastris quit one or the other. DeCastris left the police job with disability benefits, which led to this case. The police did not learn of the Zenith job until DeCastris had collected benefits for 27 months, the maximum to which an officer with DeCastris’s nine years of service is entitled. Had he disclosed that he was making more than $2,500 a month from Zenith (which he was in 1979), disability officials testified, he would not have received disability benefits.1 The crime is mail fraud, in violation of 18 U.S.C. § 1341 [263]*263(the affidavits went by mail); the sentence is two years’ imprisonment, five years’ probation, and a fine of $5,000.
DeCastris concedes that he was working full time at Zenith and that he did not reveal this employment to the officials administering the disability program.2 He insists that this is not mail fraud because both the state statute and the monthly affidavit are ambiguous. He says that an ordinary person would think that “assume” employment means “take a new job” and that “resume” employment means “go back to your old job” — neither of which he did, because he worked at Zenith without interruption. This is not a claim that De-Castris complied with state law. The head of the disability board testified that he did not, and in the district court DeCastris argued insufficiency of the evidence rather than legal error. The prosecutor’s argument is that DeCastris intentionally put the disability board off the scent, forestalling any resolution of ambiguities in the state’s law. DeCastris’s position is that state law and the affidavit were so opaque that De-Castris should not be held criminally liable for failing to alert the board to his employment.
The crime of mail fraud is a fraudulent “scheme” facilitated by use of the mails. United States v. Lindsey, 736 F.2d 433, 436 (7th Cir.1984); United States v. Feldman, 711 F.2d 758, 765 (7th Cir.), cert. denied, 464 U.S. 939,104 S.Ct. 352, 78 L.Ed.2d 317 (1983). The mailings may be innocent or even legally necessary. United States v. Green, 786 F.2d 247 (7th Cir. 1986). Here the mailings facilitated the scheme, if there was a scheme. The question whether DeCastris practiced a scheme to extract benefits to which he was not entitled is one of fact, depending on the state of his knowledge. Concealing information known to be pertinent to a proper decision may be a fraudulent scheme. Feldman; United States v. Bush, 522 F.2d 641, 646 (7th Cir.1975); United States v. Keane, 522 F.2d 534, 544 (7th Cir.1975), cert. denied, 424 U.S. 976, 96 S.Ct. 1481, 47 L.Ed.2d 746 (1976). It is a crime to lie about your income to tax officials even if you might be able to show that you owe no tax; the parallel here is that it may be mail fraud to lie about your income to disability officials and forestall any inquiry into the effect of a second job. If DeCastris knew that he had to disclose his employment, that his earnings may have mattered no matter when he started working at Zenith, then there was a scheme to defraud, and if not, not.
The instructions presented this question squarely for the jury’s decision. They told the jurors that in order to convict DeCastris they had to be convinced that he acted “knowingly and with the intent to defraud.” Another instruction elaborated, stating that knowledge means that “the [264]*264acts charged were done knowingly and with the intent to mislead the Policeman’s Annuity and Pension Board as to the defendant’s employment at Zenith Electronics Corporation, in order to cause a financial gain to defendant. Good faith is a complete defense to the charge of mail fraud.” DeCastris did not object to this instruction. The evidence, now taken in the light most favorable to the prosecution, supports an affirmative answer. DeCastris had received a letter from the disability officials stating: “in the event disability benefit payments and regular employment compensation exceed Civil Service salary, a reduction in payment of disability benefits shall be made the following month.” This letter, coupled with the evident purport of an affidavit seeking information about employment, could lead a reasonable juror to conclude that DeCastris — a police officer, the supervisor of 90 employees at Zenith, and therefore aware of the nature of bureaucratic forms in general — knew that he had to reveal information about all earnings from employment. Cf. Screws v. United States, 325 U.S. 91, 101-07, 65 S.Ct. 1031, 1035-38, 89 L.Ed. 1495 (1945).
The prosecutor bolstered the inference by showing that DeCastris lied in response to clear questions as well as cloudy ones. The judge allowed the prosecutor to introduce ten documents containing lies. One was DeCastris’s application for employment at Zenith, which claimed more education than DeCastris possessed and omitted information about his job as a police officer. DeCastris claimed to be self-employed. Most of the rest were annual questionnaires filed with the police claiming nonexistent educational credentials. The judge excluded from evidence another form in which DeCastris told the police department that he lived in Chicago (which is legally required of a Chicago police officer); DeCastris did not live in Chicago, and the judge thought this particular lie would be unduly prejudicial. See Fed.R.Evid. 403.
DeCastris’s counsel put his intent in issue by emphasizing the ambiguity of “assume” and “resume”. (DeCastris did not testify, so we do not have his own account of his mental state.) Fed.R.Evid. 404(b) allows the introduction of “other wrong” evidence to show intent, although not to show the defendant’s character. “Intent” and “character” may merge in a case such as this, however, making the application of the rule difficult. DeCastris says that the forms were used to portray him as a bad actor, likely to lie again in filling out the next form. No doubt there is something to this concern. Evidence of this type invites the inference that he who lies often ought to be damned as a liar without regard to the crime in question. On the other hand, a demonstration that DeCastris lied repeatedly in response to clear questions on other forms shows something about his intent in filling out the affidavits for the disability officials. Did he omit the information because of confusion or even a genuine belief that pre-existing jobs need not be revealed? Or did he omit the information in order to befuddle the officials and obtain benefits to which he knew he was not entitled? Evidence that DeCastris had sought to mislead through the use of other forms influences the proper understanding of his intent in filling out the affidavits.
The “bad character” inference is inseparable from the “bad intent” inference. We do not pretend that a jury can keep one inference in mind without thinking about the other. An instruction told the jury to do this,3 but this is like telling someone not to think about a hippopotamus. To tell someone not to think about the beast is to assure at least a fleeting mental image. So it is here. Each juror must have had both the legitimate and the forbidden con[265]*265siderations somewhere in mind, if only in the subconscious.
Yet this unwelcome consequence of using “other wrong” evidence does not make the evidence inadmissible. It is relevant to the outcome of the case. The risks of error are not one-sided. A jury forced to assess DeCastris’s claim of mistaken interpretation without being able to examine his history of filling out forms may have been led to error. The prosecutor could not stop with a single incorrect form. That, too, may have been chalked up to error or mistake. The relevant evidence is the pattern of lies in response to questions on forms. It is the pattern, and not an isolated episode, that helps the jury to assess DeCastris’s intent in returning the affidavits month upon month. See also, e.g., United States v. Ramsey, 785 F.2d 184, 191-92 (7th Cir.1986) (sustaining the use of evidence of lies about educational achievement as part of proof of intent); United States v. Chaimson, 760 F.2d 798, 805 (7th Cir.1985); United States v. Miller, 573 F.2d 388, 393 (7th Cir.1978). Naturally the pattern will span a course of years (otherwise it’s not much of a pattern), so the fact that the forms introduced here go as much as ten years before the first affidavit does not count against them. Cf. United States v. Lea, 618 F.2d 426, 431 (7th Cir.), cert. denied, 449 U.S. 823, 101 S.Ct. 82, 66 L.Ed.2d 25 (1980) (similar acts 10 or 12 years before the events charged); Fed.R.Evid. 609(b) (presumptive limit of ten years on age of prior convictions used to impeach a witness).
When the “other wrong” evidence is relevant to a legitimate subject such as intent, the district judge must decide how much is too much. United States v. Kane, 726 F.2d 344, 348 (7th Cir.1984); United States v. Wormick, 709 F.2d 454, 459 (7th Cir. 1983). This delicate balance of probative force against undue prejudice calls for all of the judge’s skills. The judge must enter the mind of the jurors and appreciate how a piece of eyidence fits. How the evidence fills out the picture drawn at trial, how well the jurors can suppress their natural inclinations to use the information for forbidden as well as legitimate purposes, and even more factors require an assessment of imponderables. In this case there are no clear answers, and reasonable judges could come to different conclusions. When there is no clear right and wrong, we review the decision under a deferential standard. See Metlyn Realty Corp. v. Esmark, Inc., 763 F.2d 826, 831 (7th Cir.1985); United States v. Burke, 781 F.2d 1234, 1243 (7th Cir. 1985); Ramsey, supra.
The evidence of prior lies had great potential to produce condemnation of character, which could lead to an emotional rather than reasoned conviction, but this potential was not so powerful (in relation to the legitimate value of the lies) that the district judge’s decision is beyond the pale. The judge approached the job thoughtfully, and she eliminated evidence of a lie about residence to which she thought jurors would react improperly. The line must be drawn somewhere, and when the line is drawn with care, as it was here, an appellate court may not substitute its judgment for that of the district judge. Cf. Maine v. Taylor, — U.S. —, —, 106 S.Ct. 2440, 2450-51, 91 L.Ed.2d 110 (1986); Anderson v. City of Bessemer City, 470 U.S. 564, 105 S.Ct. 1504, 1511-13, 84 L.Ed.2d 518 (1985). The district judges, specialists in applying rules to facts, generally have the last word in drawing lines where surveyors do not go. The line drawn in this case was tenable.
Affirmed.