The defendant pleaded guilty to conducting an enterprise through a pattern of racketeering, in violation of a provision of the RICO statute, 18 U.S.C. § 1962(c). He was the police chief of Northlake, a suburb of Chicago, and during his tenure in this job, which lasted from 1990 to 1994, he received some $500 a month from the "Outfit" (the Chicago branch of the Mafia, the Outfit is the lineal descendant of the Capone mob) to protect illegal gambling in the town's bars and restaurants. He was sentenced to 88 months in prison and to pay restitution to Northlake equal to a year's salary as police chief. His appeal challenges a number of the rulings of the district judge relating to his sentence.

The federal sentencing guidelines base the severity of punishment for a crime that involves taking bribes, as Sapoznik's RICO violation did, on the "benefit received" in return for the bribe. U.S.S.G. § 2C1.1(b)(2)(A) and Application Note 2; United States v. Krilich, 159 F.3d 1020, 1030-31 (7th Cir.1998). The beneficiaries here were the owners of the bars and restaurants that profited from the illegal gambling that Sapoznik protected, plus the Outfit, which took a percentage of the gambling revenues. The district court estimated those revenues at $6 million, which--if they were, as the court believed, the "benefit received" within the guideline's meaning--put Sapoznik in the $5-million-plus bracket, requiring a heavier sentence. § 2F1.1(b)(1)(O). Sapoznik challenges the $6 million figure on the ground that the government failed to show how much of it was actually due to his bribe-induced efforts to protect the illegal gambling. Maybe, since law enforcement is imperfect, there would have been illegal gambling in Sapoznik's jurisdiction whether or not he was bribed. Maybe, because of limitations on the resources allocated to law enforcement or the limitations of his own abilities, he could not have closed down the illegal gambling dens even if he had wanted to. But this is too speculative an inquiry to force on the sentencing process. To show that the bribes benefited the people paying them--here the operators of gambling dens and their gangster backers--it is enough for the government to show that the bribes facilitated the gambling operations.

But the question of causation is different, in criminal as in civil law, from the question of quantification. (In tort law the difference is between the fact of injury and the amount of damages.) It is sufficiently clear that the bribes contributed to the illegal gambling; it is profoundly unclear how much they contributed to the profits of the illegal gambling. Cf. United States v. Ellis, 951 F.2d 580, 585-86 (4th Cir.1991). The difference is critical. The government concedes that the relevant "benefit received" is indeed profit (net revenue) and not (gross) revenue. U.S.S.G. § 2C1.1, Application Note 2; United States v. Glick, 142 F.3d 520, 525-26 (2d Cir.1998); United States v. Schweitzer, 5 F.3d 44, 47 (3d Cir.1993); but cf. United States v. McAlpine, 32 F.3d 484, 489 (10th Cir.1994). But it made no effort to net out the costs associated with the gambling that the bribes facilitated. The government does not deny that it was its burden, not the defendant's, to provide evidence from which these costs could be estimated. Instead it argues that the $1 million by which the gross-revenue figure exceeded the bottom of the sentencing bracket ($6 million - $5 million) was a sufficient cushion to protect Sapoznik from being sentenced on the basis of gross rather than net. It claims that the fixed costs of the bars and restaurants should not be allocated to the gambling since, by the definition of fixed costs, they would have had to be incurred regardless of how large the firms' revenues were. Autotrol Corp. v. Continental Water Systems Corp., 918 F.2d 689, 692 (7th Cir.1990).

This won't do. We have no idea what the costs associated with the gambling activities of Northlake's bars and restaurants are and there is nothing in the record to fill the void in our knowledge. We don't even know whether these establishments paid excise taxes on their gambling revenues; excise taxes are deducted from gross revenues to determine net revenues, or profit. Commissioner v. Sullivan, 356 U.S. 27, 78 S. Ct. 512, 2 L. Ed. 2d 559 (1958); Mitchell v. Commissioner, 416 F.2d 101 (7th Cir.1969). Although the excise tax rate on illegal wagers is only 2 percent, 26 U.S.C. § 4401, the tax is on the amount wagered rather than on the gambling den's take, and we don't know what that amount was, or what the other expenses of the gambling establishments were.

The government's point about fixed costs is sound in general, see United States v. Landers, 68 F.3d 882, 884 n. 2 (5th Cir.1995), but is inapplicable to the circumstances of this case. It is true that costs that are invariant to the amount of gambling are not costs of gambling. But, for all that appears, the installation of gambling machines requires additional floor space in a bar or tavern. This would increase the fixed costs of the establishment, yet as the increase would be wholly caused by gambling--would be wholly avoidable, in other words, by a decision not to offer gambling--it would be chargeable against gambling revenues. Evidence that is in the record but was not mentioned by the district judge indicates that some bars turned to gambling because they were having difficulty making money, and these bars may have remained in business only because of their gambling revenues. If so, then some or even all of their fixed costs would have to be allocated to gambling because they would not have been incurred had it not been for the gambling. The government did deduct the money that the gamblers won, and which therefore did not enure as profit to the bars and restaurants (and the Mafia). Yet this was actually a dubious procedure, since the winnings from illegal gambling might be thought profits of gambling (albeit to the gamblers rather than to the bars and restaurants or the Mafia) rather than costs. It is apparent that the government has not thought very hard about calculating the profits of an illegal enterprise.

Were it obvious that at least 83.33 percent (5/6) of Northlake gambling revenues are net, we wouldn't insist on evidence; rough approximations, which are usually all that is available for estimating the costs of an illegal enterprise, are good enough. U.S.S.G. § 2F1.1, Application Note 8; United States v. Hang, 75 F.3d 1275, 1284 (8th Cir.1996); United States v. Landers, supra, 68 F.3d at 884 n. 2. But in this case there is not enough evidence to permit even an approximation. There is no evidence at all. Cf. United States v. Krilich, supra, 159 F.3d at 1031; United States v. Schneider, 930 F.2d 555, 558-59 (7th Cir.1991); United States v. Ellis, 951 F.2d 580, 585-86 (4th Cir.1991); United States v. Muhammad, 120 F.3d 688, 700 (7th Cir.1997).

Sapoznik next complains about the district court's having deemed his receipt of similar bribes in his previous job "relevant conduct" within the meaning of U.S.S.G. § 1B1.3(a)(2). (A critical move, because most of the $6 million in gambling revenues were earned by the bars and restaurants that he protected in his previous job.) Between 1980 and 1990 Sapoznik was police chief of another Chicago suburb, Stone Park, and he took bribes from the Outfit (indeed from the same member of the Outfit) to protect illegal gambling in Stone Park. From Stone Park he moved directly to Northlake in 1990 and without missing a beat began engaging there in the offense for which he was convicted.

The guideline defines "relevant conduct" as criminal acts "that were part of the same course of conduct or common scheme or plan as the offense of conviction." Possibilities for abuse abound if this language is given too elastic an interpretation. For then the offense of conviction becomes the handle on which the court can punish the defendant for additional crimes (though only up to the statutory maximum penalty for the offense of conviction) on the basis of a bare preponderance of evidence at a sentencing hearing in which there is no right to trial by jury or to other procedural safeguards deemed fundamental in a criminal trial. That would be the pure "real offense" (as distinct from "charge offense") sentencing system that the Sentencing Commission rejected. United States v. White, 888 F.2d 490, 496 (7th Cir.1989).

The least problematic case is one where the relevant conduct is part of the same criminal transaction that includes the offense of conviction but the transaction constitutes more than one crime yet the defendant was tried for only one. United States v. Wyss, 147 F.3d 631 (7th Cir.1998); David v. United States, 134 F.3d 470, 476-77 (1st Cir.1998); United States v. Shaw, 91 F.3d 86, 88 (9th Cir.1996). Suppose the defendant burgled a residence and then set it on fire. To try him for arson and sentence him for burglary as well would not be worrisome despite the lesser standard of proof and fewer procedural safeguards at a sentencing hearing; the trial would have brought out the facts about the burglary as well as those about the arson, since the two sets of facts would largely overlap. A little but not a lot more worrisome is the case in which the defendant has a criminal plan that unfolds over a period of time, and only one of the crimes committed pursuant to the plan is the offense of conviction. Even so, proof of the plan enables guilt of the other crimes to be inferred with confidence. See U.S.S.G. § 1B1.3, Application Note 9(A); United States v. Taylor, 72 F.3d 533, 548-49 (7th Cir.1995). Also not too worrisome is the case where the defendant goes on a spree and within a short space of time commits a series of identical crimes. U.S.S.G. § 1B1.3, application note 9(B); United States v. Rudolph, 137 F.3d 173, 176 (3d Cir.1998); United States v. Fuentes, 107 F.3d 1515, 1525 (11th Cir.1997). Once again, proof of one crime enables guilt of the others to be inferred with confidence at the sentencing hearing.

More troublesome is the situation in which the offense of conviction is successive to the relevant conduct and the sequence of offenses covers years rather than days or weeks. Cf. United States v. Patel, 131 F.3d 1195, 1203-04 (7th Cir.1997); United States v. Jackson, 161 F.3d 24, 29-30 (D.C.Cir.1998). Sapoznik was convicted of crimes committed between 1990 and 1994, but was punished for crimes reaching back as early as 1980. All the crimes, however, were committed pursuant to a single plan, involving cooperation with the Outfit in protecting illegal gambling from interference by police under Sapoznik's command.

We are not impressed by Sapoznik's argument that he was unfairly surprised when the government sprang the relevant conduct on him for the first time at the sentencing hearing. The plea agreement, which recites that it is "preliminary in nature and based on facts known to the government as of the time of the agreement," had clearly reserved this right to the government.

Sapoznik argues that the judge should not have given him additional punishment points for obstruction of justice because he concealed his Stone Park bribes from the probation service. Relying on dicta in United States v. Partee, 31 F.3d 529, 531-32 (7th Cir.1994), he argues that the only concealments that can be used as a basis for a finding of obstruction of justice are concealments of elements of the offense of conviction, which was limited to his bribe-taking at Northlake. Not so. A defendant obstructs justice not only when he makes it more difficult for the government to apprehend or (once he is apprehended) convict him, but also when he makes it more difficult for the court to give him the sentence that is his just desert. U.S.S.G. § 3C1.1 and Application Note 3(h); United States v. Wells, 154 F.3d 412, 414 (7th Cir.1998); United States v. Thomas, 11 F.3d 1392, 1400-01 (7th Cir.1993); United States v. Lange, 918 F.2d 707, 709 (8th Cir.1990). What is true but distinct is that had Sapoznik testified falsely in a prosecution for taking bribes when he was police chief of Stone Park, his false testimony could not be used to show that he obstructed justice in the present prosecution, even if that false testimony would have made it harder to establish the existence of relevant conduct. United States v. Ramunno, 133 F.3d 476, 481 (7th Cir.1998); United States v. Polland, 994 F.2d 1262, 1269 (7th Cir.1993); United States v. Self, 132 F.3d 1039, 1043 (4th Cir.1997). (United States v. Partee, supra, was such a case; its dicta have been disapproved in a recent amendment to U.S.S.G. § 3C1.1. See 63 Fed.Reg. 28202, 28206-07 (May 21, 1998).) Otherwise we might have to consider whether false testimony given in a prosecution years ago might be considered obstruction of justice in the present case, since the sentence in the present case would be influenced by the defendant's criminal record. Here, however, the false statement was given in the very sentencing proceeding that it was the intent and effect of the statement to influence in the defendant's favor.

Last is a challenge to the order of restitution. The order directs Sapoznik to restore to Northlake a year of his salary as police chief. The federal criminal code requires the sentencing judge to order a convicted defendant to "make restitution to any victim of" the offense of conviction, 18 U.S.C. § 3663A(a)(1), and a government agency can be a victim. United States v. Martin, 128 F.3d 1188, 1190-91 (7th Cir.1997). The proper amount of restitution is the amount wrongfully taken by the defendant. 18 U.S.C. § 3663A(b)(1)(B); United States v. Messner, 107 F.3d 1448, 1455 (10th Cir.1997). The government argues that Sapoznik obtained his salary from Northlake under the false pretense that he was honest. We may assume that Northlake would not have hired him had it known of his intentions, and in that event it would not have paid him four years' salary, let alone one year's. But of course it would not have "saved" all this money, or indeed any of it. It still would have needed a police chief. Presumably it would have hired an honest police chief and paid him the same as it paid Sapoznik. This makes it apparent that what Northlake lost as a consequence of Sapoznik's RICO violation was not his salary, but the difference in the value of the services that he rendered Northlake and the value of the services that an honest police chief would have rendered. The government, which had the burden of proof, 18 U.S.C. § 3664(e); United States v. Menza, 137 F.3d 533, 537 (7th Cir.1998); United States v. Messner, supra, 107 F.3d at 1455, made no effort to estimate this value. For all that appears, Sapoznik performed most of his duties as police chief in exemplary fashion.

This possibility would require vacating the order of restitution if the judge had ordered him to pay back the entire salary that he received from Northlake during the four years that he worked for the town and took bribes. But she didn't do this. She ordered him to pay back only one year's salary, that is, one fourth of his total salary from the town. Although this is an arbitrary fraction, it rather generously credits Sapoznik with being worth to the employer three-fourths of his salary even though he was corrupt. Given the difficulty of estimating the loss that he actually imposed on the city (as opposed to the gain that he conferred on the gambling dens and the Mafia), we think the district judge acted within the limits of her discretion. Seventy-five percent of Sapoznik's salary, unlike 16.67 percent of the gambling revenues, is cushion enough to keep within reasonable bounds the rough approximation that is all that is feasible in the computation of loss in a case such as this.

To summarize, Sapoznik's sentence must be vacated, though only because of the error in the computation of the net benefit generated by the bribes, and the case remanded to the district court for resentencing.

VACATED AND R EMANDED.