EASTERBROOK, Circuit Judge.

Thomas Hawkins and John Racasi were employed as analysts on the staff of Larry Rogers, a member of the Cook County Board of Review, when they accepted money from Ali Haleem, a corrupt Chicago police officer acting as an undercover agent in order to reduce the penalties for his own crimes. The Board of Review hears complaints by property owners who believe that the assessed valuation (which affects real-estate taxes) is excessive. Haleem paid Hawkins and Racasi to arrange for lower assessments. They took his money, and the assessments were reduced, except for one parcel about which the protest was untimely. A jury found that Hawkins and Racasi had violated 18 U.S.C. § 666 (theft or bribery concerning programs receiving federal funds) and § 1341 (mail fraud), plus corresponding prohibitions of conspiracy. Hawkins and Racasi contend that they committed a different offense — they assert that they took the money with the intent to deceive Haleem and did nothing in exchange for the cash — and that the jury convicted them of the indictment's charges only because it was improperly instructed. The parties agree that Cook County is covered by § 666 and that the financial effect of the lower assessed valuations exceeds the $5,000 required for a conviction. Section 666(a)(1)(B) provides that any agent of a covered organization who "corruptly solicits or demands for the benefit of any person, or accepts or agrees to accept, anything of value from any person, intending to be influenced or rewarded in connection with any business, transaction, or series of transactions of such organization" commits a felony. The prosecutor contended, and the jury found, that Hawkins and Racasi took Haleem's money "intending to be influenced or rewarded" in connection with their jobs as analysts. They do not complain about the jury instruction on this element, which told the jury that it must find that they acted with one of the two forbidden intents: an intent to be influenced, or an intent to be rewarded. Their theory of defense — that they took the money planning to deceive Haleem — amounted to a confession of accepting payment with intent to be "rewarded" for their positions. This part of § 666 forbids taking gratuities as well as taking bribes. See United States v. Anderson, 517 F.3d 953, 961 (7th Cir.2008); United States v. Ganim, 510 F.3d 134, 150 (2d Cir.2007); United States v. Zimmermann, 509 F.3d 920, 927 (8th Cir.2007); United States v. Agostino, 132 F.3d 1183, 1195 (7th Cir. 1997). Contra, United States v. Fernandez, 722 F.3d 1, 22-26 (1st Cir.2013). (Defendants have not asked us to overrule Anderson and Agostino in favor of the position taken in Fernandez.) The record shows that the payments were, if not bribes, then gratuities (from defendants' perspectives) even if Haleem would have preferred to get something for his money. The jury may well have found that defendants intended to be influenced; but if they did not, then they intended to be rewarded for the positions they held, if not for services delivered. They are guilty either way.

The contrary argument rests on the word "corruptly". Hawkins and Racasi maintain that, to show that they acted corruptly, the prosecutor must prove that they took the money intending to perform an official act in exchange. The judge thought otherwise and told the jury that a covered agent acts "corruptly" if he takes money "with the understanding that something of value is to be offered or given to reward or influence him in connection with his official duties." In other words, the "corruption" entails the payee's knowledge that the payor expects to achieve a forbidden influence or deliver a forbidden reward. This definition of "corruptly" comes from the Seventh Circuit's Pattern Criminal Jury Instructions (2012 ed.) for § 666 (see page 205), which derived it from United States v. Bonito, 57 F.3d 167, 171 (2d Cir.1995). This court has used the same definition of "corruptly" in a prosecution under 18 U.S.C. § 201. See United States v. Peleti, 576 F.3d 377, 382 (7th Cir.2009).

Defendants want us to overrule Peleti and disapprove Bonito. We shall do neither. Defendants treat the word "corruptly" as effectively removing the statute's prohibition of taking money as a "reward". Using one statutory word to blot out another would be unsound. The understanding in Peleti and Bonito leaves work for all words in this statute. As defined in the instruction, agents of a covered jurisdiction act corruptly if they know that the payor is trying to get them to do the acts forbidden by the statute, and they take the money anyway. That's a sensible definition of "corruptly". As this jury was instructed, Hawkins and Racasi could be convicted only if (a) the payee intended to be influenced (that is, to perform some quid pro quo) or rewarded; (b) the payor intended to influence or reward the defendants, and (c) the payee knew the payor's intent. That is a triple safeguard against criminalizing innocent acts. (Though it does not matter to the instructions issue, we add that Haleem's payments were not small, and the recorded conversations show that they were not innocent.)

The convictions under § 1341 pose a different problem. The mail-fraud statute is not as detailed as § 666. It prohibits schemes to defraud that use the mails but does not elaborate. Hawkins and Racasi may have defrauded Haleem out of his money (this was their defense!), but that was not the prosecutor's theory. The United States relied on 18 U.S.C. § 1346, which defines scheme to defraud as including "a scheme or artifice to deprive another of the intangible right of honest services." The idea is that the employer has a right to loyalty from agents and employees, and the prosecutor contended that Hawkins and Racasi deprived Cook County of their loyal services by taking Haleem's money secretly. But "honest services" is open-ended, and in Skilling v. United States, 561 U.S. 358, 130 S.Ct. 2896, 177 L.Ed.2d 619 (2010), the Justices deflected a contention that it is so open-ended as to be unconstitutionally vague. They did this by holding that § 1346 covers only bribery and kickbacks. This means that an agent's secret receipt of a gratuity (a "reward" in the language of § 666) does not violate § 1341, for a payment that does not entail a plan to change how the employee or agent does his job is neither a bribe nor a kickback.

The district court instructed the jury that it could convict defendants under § 1341 only if they "intended to deprive another of the intangible right to honest services through bribery." So far, so good. (The instructions did not mention kickbacks, because the prosecutor did not allege any.) But the instructions then defined bribery this way:

Under this instruction, defendants committed "bribery" if they took Haleem's money "intending to be ... rewarded" for their official positions, even if they did not plan to lift a finger to reduce the properties' assessed valuations. Treating a gratuity as a bribe transgresses Skilling. The word "corruptly" in this instruction does not save it, given the way a different instruction defined "corruptly" (a subject we discussed above).

The district judge devised the definition of bribery on his own. The prosecutor had proposed this language, from the 2012 edition of the Pattern Criminal Jury Instructions:

The judge drafted an instruction that tracks § 666 (by including "reward") rather than use the circuit's pattern instruction for § 1341 because, he said, the jury would be confused if the § 666 and § 1341 charges were treated differently. Yet if the statutes are different, the jury must be told.

The United States now defends the district judge's instruction despite its use of "reward." It contends that treating a gratuity as a bribe is consistent with Skilling because, in the course of a lengthy opinion, the Supreme Court cited 18 U.S.C. § 201(b), the principal bribery statute for federal employees, see 561 U.S. at 412 & n. 45, 130 S.Ct. 2896, and § 201(b) permits conviction on proof that the defendant accepted a reward. But that's not what Skilling says. It reversed Skilling's conviction because he did not accept anything of value "in exchange for" making misrepresentations to Enron's investors. 561 U.S. at 413, 130 S.Ct. 2896. If accepting some reward were enough, then Skilling's conviction would have been affirmed — for the theory in Skilling's own mail-fraud prosecution was that he had been rewarded (by his salary) for his services during a time when Enron violated the securities laws. The Justices thought that bribery entails a quid pro quo (planned or realized), not just a receipt of money. And § 201 says the same thing. Section 201(b)(2) provides that whoever

commits bribery. Subsection (b) requires proof that the public official demanded or took money in exchange for doing or omitting some official act. Accepting a "reward" for doing something the official would have done anyway does not violate § 201(b). By contrast, § 201(c), to which Skilling did not refer when identifying "bribery", prohibits some kinds of rewards, though far from all. United States v. Sun-Diamond Growers of California, 526 U.S. 398, 119 S.Ct. 1402, 143 L.Ed.2d 576 (1999).

The United States maintains that proof of a completed exchange is not essential, and that's right. A plan to take money in exchange for an official act constitutes a scheme to defraud, whether or not the plan succeeds. We agree with this aspect of decisions such as United States v. McDonough, 727 F.3d 143, 159-60 (1st Cir.2013); United States v. Rosen, 716 F.3d 691, 700-02 (2d Cir.2013); and United States v. Bryant, 655 F.3d 232, 244-45 (3d Cir.2011), on which the prosecutor relies. But none of these opinions holds that accepting a "reward" without doing anything in exchange — or ever planning to — is "bribery" that can support a mail-fraud conviction after Skilling. That's the problem in this instruction.

The United States weakly argues that any error was harmless, but that contention relies entirely on the undisputed fact that the defendants told Haleem that payments would induce them to lower the assessments. Yet defendants contend that they were lying. If they were indeed lying, then they can't be convicted under § 1341, even though the convictions under § 666 are valid. The definition of "bribery" in the instructions allowed the jury to bypass the question whether Hawkins and Racasi were scamming Haleem rather than Cook County. The error therefore cannot be called harmless, and defendants are entitled to a new trial of the mail-fraud charges.

Because the subject may occur on resentencing — immediately if the United States elects to dismiss rather than retry the mail-fraud charges, later if a new trial is held — we discuss defendants' contention that the judge erred by enhancing their offense levels under U.S.S.G. § 2C1.1(b)(3). This provision reads: "If the offense involved an elected public official or any public official in a high-level decision-making or sensitive position, increase by 4 levels. If the resulting offense level is less than level 18, increase to level 18." The judge concluded that Hawkins and Racasi each occupied "a high-level decision-making or sensitive position". They maintain, to the contrary, that they served in menial positions with only ministerial functions.

Cook County updates real-estate assessments every three years. Taxpayers dissatisfied with a new valuation may complain to the Board of Review. Each of the Board's three commissioners employs analysts, and a protest is assigned initially to an analyst for one of the commissioners (unless the owner requests a formal hearing, as Haleem did not). Cook County assigns every parcel an index number. An analyst types the index number into a computer; the database software responds with a list of other parcels located near the one in question, together with their assessed values. The analyst is supposed to choose the other parcels most similar to the one in question; the computer then changes the assessment to make it more like the parcels selected as comparable. (Note that this compares one assessment against others, rather than the contested assessment against market transactions; we have not been asked to decide whether this is a sensible procedure.)

Data show that this procedure leads to some reduction 79% of the time, and the parties agree that commissioners tell their staffs to favor modest reductions to keep constituents happy. If the first analyst recommends a reduction, the file goes to an analyst for a second commissioner and then a third; the majority rules. Neither the second nor the third analyst repeats the work done by the first, unless something in the file suggests that comparable properties have been generated or compared improperly.

These facts set up the dispute: defendants say that analyst cannot be a "high-level" or "sensitive" position, because the software limits the choice of comparable parcels and other analysts could outvote them. (The record does not show what functions, if any, the commissioners themselves perform.) The prosecutor replied that analysts have effectively unlimited discretion to choose which parcels on the computer-generated list to use for comparison and that the choice of comparable properties determines the outcome of the owner's protest. The prosecutor illustrated this by pointing out that Hawkins told Haleem that he could reduce the assessment of a parcel substantially by comparing it with another parcel that was "just a lot." The district judge sided with the prosecutor and did not err in doing so. How much discretion a particular person possesses is a question of fact. The district judge resolved the factual dispute against defendants without committing a clear error; and given that finding the application of § 2C1.1(b)(3) is not an abuse of discretion.

It is perplexing that the parties have devoted so much attention to this subject, because the district judge imposed sentences well below the Guideline range of 33 to 41 months for each defendant: 24 months for Hawkins and 18 months for Racasi. The judge did not imply that the sentences would have been lower still, had he resolved the § 2C1.1(b)(3) issue in defendants' favor. We have encouraged district judges to bypass debatable issues in the calculation of Guideline ranges if the issues turn out not to matter, and to state on the record whether the sentence would have been the same if the debated issue had come out the other way. See, e.g., United States v. Lopez, 634 F.3d 948, 953-54 (7th Cir.2011); United States v. Sanner, 565 F.3d 400, 405-06 (7th Cir.2009); cf. Peugh v. United States, ___ U.S. ___, 133 S.Ct. 2072, 2088 n. 8, 186 L.Ed.2d 84 (2013) (a mistake in calculating the Guidelines level is harmless if the sentencing judge makes clear that the disputed issue did not affect the sentence). We encourage the district judge to follow that approach if a further dispute crops up on remand.

The § 666 convictions are affirmed and the § 1341 convictions vacated. The cases are remanded for further proceedings consistent with this opinion.