
523 F.3d 702 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Robert SORICH, Timothy McCarthy, John Sullivan, and Patrick Slattery, Defendants-Appellants.
Nos. 06-4251, 06-4252, 06-4253, 06-4254.
United States Court of Appeals, Seventh Circuit.
Argued May 1, 2007.
Decided April 15, 2008.
*704 Barry Miller (argued), Office of the United States Attorney, Chicago, IL, for Plaintiff-Appellee.
Mariah E. Moran, Stetler & Duffy, Chicago, IL, John D. Cline (argued), Jones Day, San Francisco, CA, for, Defendant-Appellant, Robert Sorich.
Patrick E. Deady (argued), Hogan Marren, Chicago, IL, for, Defendant-Appellant, Timothy McCarthy.
Cynthia L. Giacchetti (argued), Chicago, IL, for, Defendant-Appellant, John Sullivan.
Patrick W. Blegen (argued), Chicago, IL, for, Defendant-Appellant, Patrick Slattery.
Before RIPPLE, MANION, and WILLIAMS, Circuit Judges.
WILLIAMS, Circuit Judge.
Despite the existence of a federal consent decree and other measures that for decades have sought to bring more transparency *705 and legitimacy to the City of Chicago's civil service hiring, patronage appointments have continued to flourish. These defendants were key players in a corrupt and far-reaching scheme, based out of the mayor's Office of Intergovernmental Affairs, that doled out thousands of city civil service jobs based on political patronage and nepotism. The government alleged that the defendants concealed what they were doing by falsely assuring city lawyers that their hires were legitimate, and then shredding evidence and hiding their involvement once a criminal investigation began. After an eight-week jury trial, three of the defendants were convicted of mail fraud and the fourth of making materially false statements to federal investigators. The centerpiece of their appeal is a challenge to the government's theory of prosecution: they contend that their behavior, while dubious, is not criminal, and that the honest services mail fraud statute, 18 U.S.C. § 1346, is unconstitutionally vague. We conclude that the defendants' actions do constitute mail fraud, and that the statute is not unconstitutionally vague as applied to the facts of this case. The defendants also argue that they did not deprive the city or the people of Chicago of any money or property, but the jobs that they wrongfully gave away were indeed a kind of property, so we reject this argument. Individual defendants also challenge the sufficiency of the indictment, the connection to the mails, and the sufficiency of the evidence against them, while one defendant argues that he was entitled to a sentencing adjustment for playing a minor role. Finding none of these arguments persuasive, we affirm on all counts.

I. BACKGROUND
The beating heart of this fraudulent scheme was the mayor's Office of Intergovernmental Affairs (IGA). Formally, the office serves as a liaison between the City of Chicago and state and federal governments and has no role in hiring for the city's 37,000 or so civil service jobs. Informally, the office coordinated a sizeable portion of the city's civil service hiring, ferreting out jobs to footsoldiers in the mayor's campaign organization and to other cronies.
The government introduced a substantial amount of evidence describing both the contours and the details of this long-running operation (it has likely been in place since before any of these defendants came to work for the city[1]). We view the evidence in the light most favorable to the government since the jury found the defendants guilty. It includes testimony from former department heads, political campaign coordinators, personnel managers, and workers both hired and rejected; wiretaps of conversations; and documentary evidence, including hiring records, sham interview forms, and lists tracking job applicants and their sponsors. The most dramatic document is a spreadsheet showing all 5,700 patronage applicants and their sponsors between 1990 and 1997. The spreadsheet was kept on defendant Robert Sorich's laptop computer, and he attempted to destroy both the list and the computer, but both were turned over to the FBI in 1997 pursuant to a grand jury subpoena. FBI analysts were able to recover the spreadsheet.
Rather than describe this evidence in detail, we will provide an overview here, and will supply any relevant specifics in the analysis section below. Sorich was the mayor's so-called "patronage chief," and held the title Assistant to the Director of IGA. Defendant Timothy McCarthy was Sorich's deputy from 2001 to 2005 and often stepped into his shoes. Campaign *706 coordinators would pass Sorich lists of campaign workers and volunteers, whose names he would then send to the heads of various city departmentsAviation, Streets and Sanitation, Sewers, Water, etc.for jobs. Defendants Patrick Slattery and John Sullivan held high positions in the Department of Streets and Sanitation.
During both individual and mass-hiring sequences, departmental managers like Slattery and Sullivan would hold sham interviews and then falsify interview forms in favor of the pre-selected "winners." The interview forms were often filled out weeks after the interviews, with one pile for blessed applicants (to be given high scores), and another for everybody else (to be given low scores). Some positions, such as tree trimmer, required merit tests but the results were frequently ignored. Evidence showed that Sorich even pressured departmental managers to hire applicants with drinking problems for positions that involved overseeing workplace safety.
This all went on despite the existence of multiple laws and personnel regulations forbidding the use of political considerations in hiring for civil service jobs, and mandating the awarding of those jobs on merit. These laws largely stem from the "Shakman Decrees," which are two federal consent decrees banning the use of politics in City of Chicago hiring that came into being as a result of litigation in the 1970s and '80s. Members of the scheme falsely signed "Shakman certifications," attesting that particular hiring sequences had not been influenced by political patronage.
Early on, the defendants moved to dismiss the indictment. The district court denied the motion, and many of the arguments that it rejected form the basis of this appeal. During trial the government moved to dismiss its first count of mail fraud, which implicated all four defendants, based on an insufficient connection to the mails. Sorich was convicted of two counts of mail fraud and acquitted of two counts. He received a sentence of 46 months' imprisonment. McCarthy was also convicted of two counts of mail fraud and sentenced to 19 months' imprisonment. Slattery was convicted of one count of mail fraud and given a 27-month sentence, and Sullivan was convicted of one count of giving a material, false statement to the FBI, and acquitted of one count of the same. He was sentenced to 60 days' imprisonment.

II. ANALYSIS

A. Mail fraud
The indictment posited two theories of mail fraud: that the defendants defrauded the city and the people of (1) money and property, and (2) the intangible right to the defendants' honest services as city officials. The jury filled out a general verdict form that did not specify under which theory it convicted. If the defendants were mounting a factual challenge to the sufficiency of the evidence, then sufficient evidence to convict on either theory would preserve the jury's verdict. But both theories must be legally soundthe honest services statute must be constitutional, for instancein order for the guilty verdict to stand, and the defendants argue that the honest services theory was fatally flawed. See Griffin v. United States, 502 U.S. 46, 59-60, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991); Tenner v. Gilmore, 184 F.3d 608, 611 (7th Cir.1999); United States v. Sun-Diamond Growers, 138 F.3d 961, 972 (D.C.Cir.1998). We begin with that argument, and then consider the defendants' narrower challenge to the money and property theory of mail fraud.

1. Honest services mail fraud
The defendants' chief argument on appeal is that the district court's jury instructions *707 on honest services mail fraud impermissibly expand the scope of that crime beyond the statute. They also contend that the honest services mail fraud statute is unconstitutionally vague, and that only state law can supply the fiduciary duty that runs between public officials and the citizenry. Before turning to those arguments, we provide a bit of background on honest services mail fraud.

a. Background and history
The mail fraud statute, 18 U.S.C. § 1341, criminalizes the use of the mails for carrying out a "scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises." The courts had long interpreted this statute as encompassing schemes to defraud another not just of money and property, but also "intangible rights," chief among them the right of citizens to the honest discharge of public duties by public servants. The Supreme Court put an end to this theory in McNally v. United States, 483 U.S. 350, 360, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987), holding:
Rather than construe the statute in a manner that leaves its outer boundaries ambiguous and involves the Federal Government in setting standards of disclosure and good government for local and state officials, we read § 1341 as limited in scope to the protection of property rights. If Congress desires to go further, it must speak more clearly than it has.
Congress then spoke. The year after the McNally decision it passed 18 U.S.C. § 1346, which reads in its entirety: "For the purposes of this chapter, the term `scheme or artifice to defraud' includes a scheme or artifice to deprive another of the intangible right of honest services." The statute superseded McNally and reinstated the line of cases preceding it. See United States v. Rybicki, 354 F.3d 124, 136-37 (2d Cir.2003) (en banc).
Broadly speaking, honest services fraud cases come in two types. In the first, an employer is defrauded of its employee's honest services by the employee or by another. In United States v. George, 477 F.2d 508, 509-10 (7th Cir.1973), for example, an employee of television manufacturer Zenith granted a contract to another company to supply television cabinets in exchange for kickbacks. The Zenith employee, the worker at the cabinet factory, and a middleman all were convicted of depriving Zenith of its employee's honest services. In the second and more common type of case, the citizenry is defrauded of its right to the honest services of a public servant, again, by that servant or by someone else. For instance, in United States v. Warner, 498 F.3d 666 (7th Cir.2007), the Illinois Secretary of State channeled state contracts and leases to a friend in return for paid vacations.
In both examples above, and in most honest services cases, the defendant violates a fiduciary duty in return for cashkickbacks, bribes, or other payments. Not all fraud cases follow this precise pattern, as we shall see, but given the amorphous and open-ended nature of § 1346, see United States v. Brown, 459 F.3d 509, 520-21 (5th Cir.2006), courts have felt the need to find limiting principles, and ours has been that the "[m]isuse of office (more broadly, misuse of position) for private gain is the line that separates run-of-the-mill violations of state-law fiduciary duty ... from federal crime." United States v. Bloom, 149 F.3d 649, 655 (7th Cir.1998) (emphasis added). We took our language from McNally, which summed up the existing law and characterized honest services mail fraud in this way. See 483 U.S. at 355, 107 S.Ct. 2875. The limitation not only cabins zealous prosecutors by insuring *708 that not every violation of a fiduciary duty becomes a federal crime, but also reduces the risk of creating federal common law crimes, which are not permitted. Bloom, 149 F.3d at 654-55. Other courts have crafted their own limiting principles to keep § 1346 from becoming too unwieldy. The Third and the Fifth Circuits have adopted "a state law limiting principle," meaning that ordinarily, honest services mail fraud only occurs when the defendant's scheme to defraud involves a violation of state law. See United States v. Murphy, 323 F.3d 102, 116-17 (3d Cir. 2003); United States v. Brumley, 116 F.3d 728, 734-35 (5th Cir.1997) (en banc). Courts have also crafted special requirements in the limited context of honest services fraud in the private sector. See generally Kristen Kate Orr, Note, Fencing in the Frontier: A Look into the Limits of Mail Fraud, 95 Ky. L.J. 789, 797-99 (2007).
Our misuse-of-position-for-private-gain limitation has not been adopted by other circuits, and in fact has come in for its share of criticism. The Tenth Circuit, in rejecting the limitation, characterized it as an effort "to judicially legislate by adding an element to honest services fraud which the text and structure of the fraud statutes do not justify." United States v. Welch, 327 F.3d 1081, 1107 (10th Cir.2003). And the Third Circuit stated that the requirement "adds little clarity to the scope of § 1346" and is, among other things "under-inclusive" because it would not cover a situationsuch as an undisclosed conflict of interestthat does not actually yield a benefit. United States v. Panarella, 277 F.3d 678, 691-92 (3d Cir.2002). The Tenth Circuit expresses a legitimate concern, for the only elements of mail fraud are (1) a scheme to defraud (entailing a material misrepresentation), (2) an intent to defraud, and (3) the use of the mails. See 18 U.S.C. § 1341; United States v. Henningsen, 387 F.3d 585, 589 (7th Cir.2004). Nevertheless, in setting out the private gain requirement we have taken our cue from the Supreme Court's own characterization of honest services fraud in McNally, and to that extent consider ourselves in good company. But we also fear that both the Tenth and Third Circuits may have misunderstood our position to some extent. Showing misuse for private gain means showing an intent to reap private gain; it is well established that a fraudulent scheme that does not actually cause harm is still actionable. See Durland v. United States, 161 U.S. 306, 313-14, 16 S.Ct. 508, 40 L.Ed. 709 (1896); United States v. Tadros, 310 F.3d 999, 1006 (7th Cir.2002).

b. Private gain
The defendants' chief argument centers on the "private gain" requirement. The district court's jury instruction stated that a scheme to defraud requires an intent "to deprive a governmental entity of the honest services of its employees for personal gain to a member of the scheme or another" (emphasis added). The defendants contend that the "or another" language misstates Bloom, which, they say, teaches that only a scheme to enrich the defendant or his co-schemers qualifies as a frauda scheme to enrich a third party does not count. The distinction is critical, because here the defendants are charged not with enriching themselves but with enriching (with jobs) thousands of individuals who worked for the campaigns of the defendants' paymasters. The "winners" of jobs were not charged with crimes, and it may not be fair to characterize them as co-schemers; there certainly are a lot of them. The government argues that if indeed the "or another" language is a mistake, the error is harmless, because here the defendants themselves achieved a gainjob security for keeping the patronage machine running. But our recent decision in United States v. Thompson, 484 *709 F.3d 877, 882 (7th Cir.2007), holds that job security is not a private gain, so if private gain by the campaign workers-turned city employees is insufficient, then the jury instruction does indeed present a problem.
The defendants' argument that any private gain must go to the defendants themselves is not without basis, for we and other courts have not always been consistent with our description of the requirement. Although McNally itself and the key portions of Bloom refer to "private gain," Bloom also once uses the phrase "personal gain," 149 F.3d at 657, and in United States v. Hausmann, 345 F.3d 952, 956 (7th Cir.2003), we used "personal gain" exclusively. Other circuits have also described our requirement as a "personal gain" or "personal benefit." See Brown, 459 F.3d at 520; Welch, 327 F.3d at 1106; Panarella, 277 F.3d at 692. The semantic difference between "private" and "personal" gain may be insignificant, but to the extent that "personal" connotes gain only by the defendant, it is misleading. By "private gain" we simply mean illegitimate gain, which usually will go to the defendant, but need not.
Imagine scenario (A) in which a mayor surreptitiously channels city contracts to his cronies in the business community; they get a windfall whereas he has merely helped his friends and takes no money. Or imagine scenario (B) in which an attorney bribes a court in order to obtain favorable results for his clients in their lawsuits. Or scenario (C) where a union boss sells union property to a senator even though the senator did not offer the highest price, and in exchange receives the senator's vote on a matter that concerns the union. In all three scenarios the public has been defrauded of the honest services of its public servants: the mayor, the court, and the senator. Moreover, in all three scenarios the defendantthe mayor, the attorney, and the union bosswas not the one who stood to gain financially. Certainly the defendants all received something: in (A), the mayor received the gratitude of his friends; in (B), the attorney could boast to future clients of a high success rate, which is good for business; and in (C) the union boss curried valuable favor with the senator. But the money went to another party. All three scenarios have played out in the federal courts and have resulted in convictions for mail fraud. See United States v. Fernandez, 282 F.3d 500, 503-05 (7th Cir.2002), United States v. Silvano, 812 F.2d 754, 759-60 (1st Cir. 1987) (scenario A); Ginsburg v. United States, 909 F.2d 982 (7th Cir.1990) (scenario B); Lombardo v. United States, 865 F.2d 155, 159-60 (7th Cir.1989) (scenario C).
These cases are the exception to a rule of human nature rather than of law: usually someone up to no good will be out to enrich himself, not others. It is thus with a hint of irony that we stated in United States v. Spano, 421 F.3d 599, 603 (7th Cir.2005), that "[a] participant in a scheme to defraud is guilty even if he is an altruist and all the benefits of the fraud accrue to other participants." The defendants seize on Spano's "other participants" language and contend that fraud exists when private gain goes to other schemers, as in the above three examples, but not when it goes to third parties. We disagree. It is much less likelybut no less culpablethat fraudulent schemers will share the proceeds with third parties rather than amongst themselves. In Hausmann, 345 F.3d at 954, 956, an attorney referred clients to a chiropractor friend in exchange for a percentage of the business brought in by each referral; he did not tell his clients about his take. The chiropractor made good by paying the attorney's creditors and his favorite charities, and we affirmed the attorney's conviction. Id. But suppose the attorney had stated that he only wanted the kickbacks to go to charities, or, for *710 that matter, to his estranged brother, about whom the attorney had always felt guilty. Unlikely scenarios, maybe, but mail fraud nevertheless. Robin Hood may be a noble criminal, but he is still a criminal. "In the case of a successful scheme, the public [or client] is deprived of its servants' [or attorney's] honest services no matter who receives the proceeds." Spano, 421 F.3d at 603.[2]
Reading Bloom's private gain requirement to include gain by non-schemers does not, as the defendants warn, "effectively eliminate[ ]" this limit on the scope of honest services mail fraud. As we have noted, it will be a rare case when a party engaged in fraud directs the benefits to non-schemers. Indeed, here, the individuals who received city jobs in return for political work may well have known that the game was rigged, but the sheer scale of the fraud (well over 5,000 jobs) might prevent a prosecutor from pursuing them in addition to the ringleaders. Moreover, the true purpose of the private gain requirementand one that does not depend on who gets the spoilsis to prevent the conviction of individuals who have breached a fiduciary duty to an employer or the public, but have not done so for illegitimate gain. Cf. United States v. Czubinski, 106 F.3d 1069, 1077 (1st Cir.1997) (mail fraud conviction reversed where IRS employee improperly accessed confidential tax records but did not misuse them for gain in any way); see also Brown, 459 F.3d at 522 (employees who engaged in fraudulent transaction to inflate their company's earnings statements did not deprive employer of their honest services because employer encouraged the misbehavior).
The defendants also contend that United States v. Thompson compels a decision in their favor. There we reversed the mail fraud conviction of Wisconsin procurement officer Georgia Thompson, who was in charge of awarding a contract for the state's travel needs. Thompson forced a run-off between her boss's contractor of choice, Adelman Travel Group, and another bidder that came out slightly ahead in a highly subjective scoring process. The two companies tied in the run-off and Thompson broke the tie in Adelman's favor according to approved procedures. Her boss was happy and she received a small raise through normal channels, but we held that this was not the sort of "private gain" that was necessary to sustain a conviction for mail fraud. 484 F.3d at 884. We did not expressly discuss the possibility that the benefit of the contract to Adelman, a third party, could be construed as the necessary private gain, but we needn't have, for the point that distinguishes Thompson from this case is the absence of a scheme to defraud. Despite the government's zealous presentation of the case, we were not convinced that Thompson engaged in fraudulent behavior, instead characterizing her acts as "conduct that, as far as this record shows, was designed to pursue the public interest as the employee understood it." Id.; see also United States v. Segal, 495 F.3d 826, 834 (7th Cir.2007) ("The case against Thompson simply did not measure up.").
*711 The present case, by contrast, features a massive scheme to defraud, complete with specific intent and material misrepresentations. The defendants created an illegitimate, shadow hiring scheme based on patronage and cronyism by filling out sham interview forms, falsely certifying that politics had not entered into their hiring, and covering up their malfeasance. These are the hallmarks of a fraud. See United States v. Bush, 522 F.2d 641, 647-48 (7th Cir.1975). Thompson is miles away.

c. Constitutionality of 18 U.S.C. § 1346
The defendants next contend that the honest services mail fraud statute is unconstitutionally vague as applied to their case. They argue that they were not on notice that their behavior was illegal, and that the government's interpretation of the statute is open to prosecutorial overreaching. Again we must disagree.
It is hard to take too seriously the contention that the defendants did not know that by creating a false hiring scheme that provided thousands of lucrative city jobs to political cronies, falsifying documents, and lying repeatedly about what they were doing, they were perpetrating a fraud. Indeed, the specific intent requirement of mail fraud seriously undercuts any claim to a lack of notice that their behavior was criminal. See United States v. Hasner, 340 F.3d 1261, 1269 (11th Cir.2003). And although the defendants insist that this prosecution is "an unprecedented expansion" of honest services mail fraud, several cases on the books provided them ample warning that they risked prosecution. United States v. Dvorak, 115 F.3d 1339, 1341 (7th Cir.1997), involved a similar patronage-in-hiring scheme in which the Undersheriff of Cook County, Illinois falsified records to cover his tracks. The defendants argue that the defendant there pled guilty and his appeal only concerned his sentence, but the fact remains that he was prosecuted and convicted of mail fraud for acts remarkably similar to theirs, and they should have taken note. More recently, United States v. Fernandez involved a sham system for awarding city contracts that closely tracks these defendants' system for awarding jobs: there was a rigged bidding process, blank questionnaires filled out after decisions had been made, and even the organization of businesses after their owners had received contracts. 282 F.3d at 503-05. These decisions provided sufficient notice.
An en banc panel of the Second Circuit recently stated that "[n]o circuit has ever held . . . that section 1346 is unconstitutionally vague." Rybicki, 354 F.3d at 143. That statement involved an asterisk, because the Second Circuit had just a year earlier held that the provision was unconstitutionally vague as applied to the facts of that case. See United States v. Handakas, 286 F.3d 92, 112 (2d Cir.2002). But Rybicki explicitly overruled that portion of Handakas, Rybicki, 354 F.3d at 144, bringing the circuit into line with the other circuits that have rejected vagueness challenges to § 1346, including our own. See Warner, 498 F.3d at 697-99; Hausmann, 345 F.3d at 958 (7th Cir.2003); Hasner, 340 F.3d at 1269 (11th Cir.2003); Welch, 327 F.3d at 1109 n. 29 (10th Cir.2003); United States v. Frega, 179 F.3d 793, 803 (9th Cir.1999); United States v. Frost, 125 F.3d 346, 371 (6th Cir.1997); United States v. Gray, 96 F.3d 769, 776-77 (5th Cir. 1996); United States v. Bryan, 58 F.3d 933, 941 & n. 3 (4th Cir.1995), abrogated on other grounds by United States v. O'Hagan, 521 U.S. 642, 650, 117 S.Ct. 2199, 138 L.Ed.2d 724 (1997). Section 1346 is not unconstitutionally vague as applied to this case.

d. Source of fiduciary duty
The defendants next argue that the indictment and the jury instructions *712 impermissibly stated that the Shakman consent decree was one of the sources creating a fiduciary duty between the defendants and the citizenry. We review this challenge de novo.
There are actually two Shakman decrees, one entered in 1972 and one in 1983, and both are the result of litigation by Michael Shakman, an independent candidate for the Illinois Constitutional Convention who felt locked out of the campaign process because of the City of Chicago's patronage hiring system. See generally O'Sullivan v. City of Chicago, 396 F.3d 843, 847-50 (7th Cir.2005). Somewhat simplified, the decrees forbid the city from basing its hiring decisions for civil servants on political factors.
Both the indictment and the jury instructions in this case describe the Shakman decrees alongside other sources of local and state law as potential sources of the fiduciary duty running between the defendants as public servants and the people of Chicago. Those sources include a state law and a local ordinance criminalizing false entries by local government officials intending to defraud, 720 ILCS 5/33E-15; Chicago, Ill.Code § 2-74-090(B), and a local ordinance mandating the selection of civil servants based on merit, Chicago, Ill.Code § 2-74-050(3). On appeal the defendants do not contest that they violated these legal provisions.
The defendants nevertheless contend that the Shakman decrees are an impermissible source of a fiduciary duty, and that since the jury did not indicate which source it relied upon, the verdict must be overturned. But we have never held that only state law can supply a fiduciary duty between public official and public or between employee and employer in honest services cases. See Bush, 522 F.2d at 646 n. 6. Indeed, our case law, and the case law of the vast majority of circuits, shows that other sources can create a fiduciary obligation. E.g., George, 477 F.2d at 514 n. 7 (employee handbook); United States v. Williams, 441 F.3d 716, 723-24 (9th Cir. 2006) (power of attorney agreement). It may well be that merely by virtue of being public officials the defendants inherently owed the public a fiduciary duty to discharge their offices in the public's best interest. See United States v. deVegter, 198 F.3d 1324, 1328 (11th Cir.1999).
The defendants invite us to adopt the minority "state law limiting principle" shared by the Third and Fifth Circuits, Murphy, 323 F.3d at 116-17; Brumley, 116 F.3d at 734, but we have already declined to add this limiting principle to the private gain requirement that stems from McNally. See Bloom, 149 F.3d at 654-55. Moreover, although in United States v. Martin we remained open to an argument on this front in the future, we also stated that "[a] litigant who wants us to overrule our previous decisions must do more than cite a recent decision of another court (unless the Supreme Court!) that is to the contrary." 195 F.3d 961, 967 (7th Cir. 1999). That is essentially all that the defendants have done here. Given this fact, and the other sources of a fiduciary duty, we decline to overturn the verdict on this basis.

2. Traditional mail fraud
In addition to challenging the government's theory of honest services mail fraud, the defendants attack the alternate theory that they committed what might be called traditional mail fraud. We review de novo their contention that the indictment insufficiently alleged a deprivation of money or property. See United States v. Moore, 446 F.3d 671, 676 (7th Cir.2006).
By setting up a false hiring bureaucracy the defendants arguably cheated the city out of hundreds of millions of dollars. The defendants argue that since the city *713 would have filled these jobs and paid these salaries anyway, it has not suffered a loss. But we rejected this argument in United States v. Leahy, 464 F.3d 773, 787-89 (7th Cir.2006), in which we upheld the conviction of a Chicagoan who obtained millions of dollars in city contracts by falsely certifying his businesses as minority-owned enterprises. We were unpersuaded by his contention that since the city would have awarded the contracts to someone, no harm was done: the "object was money, plain and simple, taken under false pretenses from the city in its role as a purchaser of services." Id. at 788; see also Hausmann, 345 F.3d at 957 (the lawyer who referred clients to a chiropractor buddy in return for kickbacks "deprived his clients of their right to know the truth about his compensation"); Welch, 327 F.3d at 1108; Bush, 522 F.2d at 648. In Leahy the city paid for, and was cheated out of, minority-owned enterprises, and here the city paid for, and was cheated out of, qualified civil servants.
Jobs are a lot like contracts. Neither is a bag full of money but both are immensely valuable: a contract is a promise to pay for services rendered, while a job is the exchange of labor for a paycheck. Hence just as Leahy held that fraudulently obtained contracts are property, courts have found that salaries fraudulently obtained, United States v. Doherty, 867 F.2d 47, 56, 60 (1st Cir.1989) (Breyer, J.), and job opportunities fraudulently denied, United States v. Douglas, 398 F.3d 407, 417-18 (6th Cir.2005); United States v. Granberry, 908 F.2d 278, 280 (8th Cir.1990), represent property for purposes of mail fraud. The defendants argue that the right to give out jobs is a mere regulatory interest of the kind that Cleveland v. United States, 531 U.S. 12, 20-21, 121 S.Ct. 365, 148 L.Ed.2d 221 (2000), said cannot give rise to a property right. But the Court in Cleveland held that a video poker license granted by the state is not property, and we think the jobs at issue here are much closer to contracts than poker licenses.
The defendants also point to United States v. Walters, 997 F.2d 1219 (7th Cir. 1993), which they say counsels that if the money or property doesn't go to the defendants, it doesn't amount to mail fraud. In Walters, we reversed the conviction of a sports agent who signed college athletes, in contravention of NCAA rules. The theory of prosecution for mail fraud was that since the agent caused the players to become ineligible (college athletes aren't allowed to have agents), he committed mail fraud every time the universities subsequently sent scholarship checks to the athletes by mail. We stated that the universities "were not out of pocket to Walters; he planned to profit by taking a percentage of the players' professional incomes, not of their scholarships." Id. at 1224. But this was not a requirement that the defendant receive the money or property, but rather a way of illustrating a deeper problem with the case. The scholarship money that the university sent the athletes was incidental, rather than the target of the scheme. See id. at 1224-25 (mail fraud statute punishes "schemes to get money or property by fraud rather than methods of doing business that incidentally cause losses"). Here, however, getting the city to award jobs to political workers and cronies was the very object of the defendants' scheme.
In sum, we hold that jobs are property for purposes of mail fraud, and that the indictment sufficiently alleged a deprivation of property.

3. Other matters pertaining to mail fraud and the indictment
Sorich, McCarthy, and Slattery raise a host of other challenges to their convictions. We find these arguments unpersuasive, and briefly discuss those substantial enough to warrant written comment.


*714 a. Use of the mails
McCarthy contends that insufficient evidence ties the use of the mails to his two counts of conviction. With respect to count two, Dennis Henderson testified that he received a job in the Sewers Department in return for political work, and for count five, Jeffrey Harness, an ordinary applicant, testified that he was passed over for a job as a building inspector. Both Henderson and Harness testified that they received their letters in the mail. McCarthy challenges this point, suggesting that the letters may have been hand delivered, but we will not overturn the jury's decision to credit Henderson's and Harness's testimony. McCarthy also contends that the Harness letter was insufficiently connected to the hiring scheme because Harness received it after the illegitimate "winner" of the position was found out and forced to resign in disgrace. But the overall hiring scheme continued, and this paperwork lent a false air of propriety and regularity to the city's hiring process. See Fernandez, 282 F.3d at 508.

b. Joining the scheme
Slattery argues that insufficient evidence shows that he joined the fraudulent scheme and possessed the specific intent to defraud. The argument has very little merit. To start with, Slattery personally falsified hundreds, if not thousands, of interview forms. He contends that "the forms cannot be accurately described as true or false," but this is a bit too philosophical for us, as we suspect it was for the jury. The forms contained numerical scores for such categories as, in a truck driver hiring sequence, driving ability and past driving experience. Although these criteria are perhaps subjective, filling them out willy-nilly and dozens at a timehigh scores for blessed applicants, low scores for the rest, without even an attempt to quantify their skillscan fairly be described as falsification.
The government presented other damning evidence of Slattery's participation and his intent to defraud. A union complained after its members did poorly in one hiring sequence, and one of the city's labor liaisons asked Slattery for the interview forms to back up the city's hiring decisions. Only one problem: the interview forms had not been completed yet. According to the liaison's testimony, after Slattery delivered this "shocking" news, she said, "Pat, please tell me you had a legitimate business reason for selecting the people that you selected. Did you base it on performance, attendance, anything?" She testified that Slattery replied, "no." On appeal, Slattery attacks her credibility, but we will not upset the jury's decision to believe her.
Slattery also pleads ignorance, saying that no juror could have found that he even knew that a fraudulent hiring system was afoot, let alone joined it. We think the jury was well-supported in rejecting this contention. Slattery and Sorich were good friends, and Daniel Katalinic, a former deputy commissioner of Streets and Sanitation who ran a political organization, testified that he overheard Slattery complain that his own political workers were not getting choice enough jobs, and that he would talk to Sorich about the matter. Katalinic also testified, as did Slattery's boss Jack Drumgould, that Slattery accompanied Drumgould to meetings in which Sorich would hand out a group of blessed applicants, and that Slattery sometimes took names directly from Sorich and passed them on to Drumgould for hiring. A reasonable jury could find beyond a reasonable doubt on this evidence that Slattery joined the scheme with an intent to defraud.

c. Sufficiency of indictment's mail fraud counts
Sorich and McCarthy contend that the district court abused its discretion by *715 refusing to dismiss a portion of the indictment that the government amended by superseding indictment thirteen days prior to trial. The government contends that after reviewing its trial proof, it decided to substitute one mailing for another on count two in order to strengthen its case and to avoid having to rely on a witness with shaky credibility. The defendants can neither show that this minor change prejudiced them in any concrete wayby demonstrating, for example, that their attorney was unable to prepare in timenor rebut the government's explanation that it simply wished to tighten its case. They have failed to make out a due process claim on this point. See United States v. McMutuary, 217 F.3d 477, 481-82 (7th Cir.2000).
McCarthy argues that count fivewhich charged mail fraud in the hiring of two unqualified union officials' sons as building inspectorswas inconsistent with the remainder of the indictment. The indictment charged a scheme of false hiring exclusively for political campaign work, he argues, whereas in this count, hiring was based on nepotism. But as in United States v. Stout, 965 F.2d 340, 344 (7th Cir.1992), McCarthy's "interpretation of the indictment is too narrow." In the very first paragraph of the indictment's "overview of the scheme" section, this text appears: "In addition, in some cases Sorich and others rewarded other favored persons and groups with City jobs and promotions." Fairly read, the scheme set out in the indictment is fraudulent hiring of croniesusually political cronies, but not alwaysand count five fits in this scheme.

B. False statements
John Sullivan was charged with one count of mail fraud and two counts of knowingly making materially false statements to the FBI, 18 U.S.C. § 1001(a)(2). At trial, the government moved to dismiss the mail fraud count  which pertained to all four defendants  after discovering that there was an insufficient connection to the mails. The jury then found Sullivan guilty of one count of making false statements and acquitted him of the other. He contends that insufficient evidence supported the conviction, that his answers were literally true if unresponsive, and that a fatal variance existed between the indictment and the proof at trial. We review whether the evidence, taken in the light most favorable to the government, could allow a rational jury to find guilt beyond a reasonable doubt. See United States v. Orozco-Vasquez, 469 F.3d 1101, 1106 (7th Cir. 2006).
Sullivan was interviewed three times by Assistant United States Attorneys and FBI agents. At that early point in the investigation, the agents focused their questioning on the city's "hired truck" scandal, which turned out to be the wedge that allowed prosecutors to split the log of fraudulent city hiring. See generally United States v. Boyle, 484 F.3d 943, 944 (7th Cir.2007). Nevertheless, they did ask about patronage in hiring, and specifically about the clout of Daniel Katalinic, who as mentioned above ran a political organization and was the Assistant Commissioner for the Department of Streets and Sanitation. Katalinic was originally indicted with these four defendants, but he pled guilty and cooperated with the government.
At trial the government elicited the specifics of Sullivan's February 18, 2005 interview through the testimony of FBI Agent John Hauser, who was present and took notes:
Government: Now, sir, what, if anything, did he say about Mr. Katalinic's political organization or getting preferential treatment in the hiring process?
Hauser: He said that to hishe didn't have any knowledge about members *716 of Katalinic's political organization getting preferential treatment.
. . .
Government: What, if anything, did he say about his knowledge of membership of the Katalinic organization?
Hauser: He said he didn't know who the members of Mr. Katalinic's organization were.
These two statements make up the count of conviction for false statements. The indictment describes the false statements as "A. Sullivan had never heard of members of Katalinic's organization getting preferential treatment; and B. Sullivan did not know the identity of members of Katalinic's organization."
During the cross-examination of Agent Hauser, the defense emphasized that he did not record the conversation verbatim, but rather used his notes to refresh his recollection on the stand, and that he did not write up his formal report of the interview until five and a half months later. (Hauser testified that it was not his usual practice to wait so long, but that there "was an intense amount of activity in the investigation at that point.") The defense also pinned Hauser down on what exactly his noteswhich were not introduced into evidencesaid. According to testimony, the notes read as follows:
Q: Never heard of DK's political people getting good treatment?
A: Doesn't know who they are.
We reject Sullivan's argument that there was insufficient evidence for the jury to find that he knowingly and willfully made false material statements about his knowledge of Katalinic's organization. See United States v. Humphrey, 34 F.3d 551, 556 (7th Cir.1994). Sullivan says he was unaware of a shadow hiring system, but the testimony of several witnesses, including Katalinic and Drumgould, showed that Sullivan complained about various IGA picks, instructed others to interview and hire certain individuals, passed on IGA candidates to those with hiring authority, and discussed members of Katalinic's political organization, including Pat Foy, a close friend of Sullivan's and a member of Katalinic's organization who testified for the government. Thus it is telling that during his three interviews with Assistant U.S. Attorneys and FBI agents, Sullivan never mentioned IGA or the role of politics in hiring decisions, despite ample opportunities to do so. With particular regard to Katalinic's political workers, testimony tied Sullivan to a list of Streets and Sanitation interviewees, complete with a color-coded key matching favored applicants with powerful sponsors, including "Dan K." Foy testified that the key was in Sullivan's handwriting. The jury was permitted to conclude that Sullivan knew the identities of members of Katalinic's organization, and that Sullivan knew that they were getting jobs and promotions.
Sullivan also contends that he was entitled to an instruction under Bronston v. United States, 409 U.S. 352, 93 S.Ct. 595, 34 L.Ed.2d 568 (1973), which reversed the perjury conviction of a man who during a bankruptcy application answered a question in a way that was literally true but unresponsive. As discussed above, the evidence was sufficient to allow a jury to find that Sullivan's statements were false rather than literally true but misleading, so the district court did not err by rejecting the instruction. As for there being a fatal variance between the indictment's description of the false statements and the evidence given at trial, Sullivan argues that "[t]here is an obvious and important difference between `having heard of' something and `having any knowledge about' something." (The indictment charged Sullivan with saying he "had never heard of" Katalinic's men getting favorable treatment, while Hauser testified that *717 Sullivan said "he didn't have any knowledge about" them getting preferential treatment.) But Sullivan doesn't say what that "obvious and important difference" is. Only a material variance between indictment and trial proof warrants relief. See United States v. Bhagat, 436 F.3d 1140, 1146-47 (9th Cir.2006); United States v. Shah, 44 F.3d 285, 296 (5th Cir.1995). Finally, Sullivan argues that Hauser's questions were fundamentally ambiguous and untrustworthy, given his reliance on his notes rather than a transcript or recording of the interview. But there is no requirement that a conversation be transcribed or recorded in order to support a conviction under § 1001, see United States v. Poindexter, 951 F.2d 369, 387-88 (D.C.Cir. 1991), and Hauser's trustworthiness was a matter for the jury, not a reviewing court.

C. Sentencing
Only one defendant challenges his sentence. Slattery argues that the district court clearly erred by refusing to grant him a two-point reduction for being a "minor participant" in the hiring scheme. U.S.S.G. § 3B1.2(b). The Sentencing Guidelines explain that to qualify for the adjustment, the defendant must be "substantially less culpable than the average participant," and "less culpable than most other participants." Id. cmt. nn. 3(A), 5. We rarely accept such challenges, given that the district court is in the best position to evaluate a particular defendant's role in a criminal scheme. See United States v. McGee, 408 F.3d 966, 988 (7th Cir.2005); United States v. Rodriguez-Cardenas, 362 F.3d 958, 959-60 (7th Cir. 2004).
We cannot agree with Slattery that he was substantially less culpable than the average participant in the hiring scheme. He was certainly less involved than Sorich, who oversaw all hiring. But the fraud could not have succeeded without high-level players in each department willing to organize sham interviews and hire the blessed candidates. In other words, the scheme required both a chief executive and mid-level management. See United States v. Gallardo, 497 F.3d 727, 741 (7th Cir. 2007) (essential member of scheme not entitled to adjustment even though others were more involved); United States v. Olivas-Ramirez, 487 F.3d 512, 516 (7th Cir. 2007) (same). Slattery protests that he only contributed to the scheme for part of its duration, but that argument is tough enough when one is involved for only two days, Olivas-Ramirez, 487 F.3d at 515-16, let alone the five years that Slattery participated. We also note that Slattery was personally responsible for providing false information on hundreds if not thousands of interview forms, behavior that belies a suggestion that he was a bit player. The district court did not clearly err in denying his request for a minor-role adjustment.

III. CONCLUSION
For the foregoing reasons, we AFFIRM the convictions and sentences of the defendants.
NOTES
[1]  See generally O'Sullivan v. City of Chicago, 396 F.3d 843, 847-50 (7th Cir.2005).
[2]  The defendants contend that this discussion in Spano is dictum, but an alternate ground for a holding is not a dictum. Woods v. Interstate Realty Co., 337 U.S. 535, 537, 69 S.Ct. 1235, 93 L.Ed. 1524 (1949); Neiman v. Rudolf Wolff & Co., 619 F.2d 1189, 1193 n. 4 (7th Cir.1980); Medeiros v. Vincent, 431 F.3d 25, 34 (1st Cir.2005). Although we eventually concluded in Spano that the defendant arguably did benefit personally, we mentioned that fact second and in a single sentence after discussing the impact of a lack of personal gain for over a paragraph. Spano, 421 F.3d at 602-03. In any case, whether or not the discussion is binding precedent, it is consistent with our case law and our understanding of the mail fraud statute, and to that extent is persuasive authority.
