POSNER, Circuit Judge.

These consolidated appeals raise significant issues regarding the scope of important federal criminal laws, and lesser evidentiary and procedural questions, all growing out of a theft of tiles that the Chicago Housing Authority had bought with federal money.

James Harris, a CHA employee for more than 20 years, was in charge of, and Richard Gray a member of, a team assigned to lay tile in public housing owned by the CHA. The materials for the project were paid for entirely by a grant from the Department of Housing and Urban Development; and although the CHA contributed the labor for the project, HUD paid for 60 percent of the CHA's operating expenses, including Harris's and Gray's wages. Theft of CHA property was suspected. An undercover agent, Matthews, asked around about hiring workers to renovate his home, and a man named Spencer referred Matthews to Harris. Matthews and Spencer met with Harris at the Chicago townhouse where supposedly Matthews lived. Harris offered to tile the kitchen and bathroom floors for $260. He wanted Matthews to see the tile he would use and therefore asked him to come the next day to an address that turned out to be that of the CHA housing project where Harris was working. There, in the presence of Gray, Harris asked Matthews to give Gray the key to the townhouse. The next day Matthews saw six boxes of tile in the townhouse, one of them open. A box full of new tiles is worth $17.28, so if all of the boxes were full their total value was $103.68. Harris and Gray completed the tile job that day, but two of the six boxes were not used and Gray gave them to Matthews. The next day Matthews paid Harris $260, and Harris gave $75 to Gray.

The indictment charged Harris and Gray each with one count of embezzling tile belonging to HUD worth more than $100, in violation of 18 U.S.C. § 657, which so far as relevant here provides that "Whoever, being an officer, agent or employee of or connected in any capacity with [HUD] . . . embezzles, abstracts, purloins or willfully misapplies any moneys, funds, credits, securities or other things of value belonging to [HUD] . . . shall be fined not more than $5,000 or imprisoned not more than five years, or both; but if the amount or value embezzled . . . does not exceed $100, he shall be fined not more than $1,000 or imprisoned not more than one year, or both." The indictment also charged each of the defendants with one count of violating 18 U.S.C. § 371, which makes it a felony for "two or more persons [to] conspire either to commit any offense against the United States, or to defraud the United States," but further provides that if "the offense, the commission of which is the object of the conspiracy, is a misdemeanor only, the punishment for such conspiracy shall not exceed the maximum punishment provided for such misdemeanor." Both defendants were found guilty in a bench trial of the offenses charged. Harris was fined $1,000, and placed on probation for two years, on each count, the sentences to run concurrently. Gray was given concurrent sentences of a year's probation on each count.

Section 657, a consolidation of eleven federal criminal statutes, punishes embezzlement and willful misapplication by officers, agents, etc. of several different federal agencies that extend credit in various forms, and of some private but federally insured financial institutions, mainly savings and loan associations. A number of other statutes apply similar prohibitions to officers, agents, etc. of other federal agencies, of federally insured banks, and of various federal contractors. See 15 U.S.C. § 645(b), 714m(b); 18 U.S.C. § 656, 665; 25 U.S.C. § 450d; 42 U.S.C. § 3220(b). In all of these and several other federal criminal statutes (see 12 U.S.C. § 631; 18 U.S.C. § 1006, 1904) the same expression — "connected in any capacity with" — is used to round out the prohibition against theft or fraud by an officer, director, agent, or employee of the institutions protected by the statute. We must decide whether Harris and Gray, who were employees of a state agency that received 60 percent of its operating funds from the Department of Housing and Urban Development and who when they (allegedly) embezzled HUD property were working on a project the materials for which had been paid for 100 percent by HUD, were connected with HUD in any capacity.

Read naturally, as well as literally, the words cover Harris and Gray. Their wages were paid in major part out of funds provided by HUD and they were working on a project the materials for which were paid for entirely by HUD. Although not technically agents of HUD, they were doing its work. Their connection to HUD was as close as the connection of the defendant in United States v. Coleman, 590 F.2d 228 (7th Cir. 1978), to the agency from which he had embezzled funds in violation of a statute worded almost identically to section 657. This is 18 U.S.C. § 665, which punishes embezzlement, etc., by whoever is "an officer, director, agent, or employee of, or connected in any capacity with any agency receiving financial assistance under the Comprehensive Employment and Training Act." Although Coleman was an employee of the General Services Department of the City of Gary rather than of Gary Manpower, the agency that had received the CETA grant, he was the Department's assistant director and the Department had agreed to use some of the people whom Gary Manpower was training with its CETA grant. These facts created a sufficiently close connection between Coleman and Gary Manpower to satisfy section 665. See 590 F.2d at 231 (alternative holding); also United States v. Pintar, 630 F.2d 1270, 1282 and n. 16 (8th Cir. 1980).

The federal government has a greater interest than the states in deterring the embezzlement of federal property (whether the tiles in this case were federal property is discussed next); and the danger of embezzlement is no less when the embezzler happens to be an employee not of the federal agency that owns the property but of a contractor who has custody of it. We are not much troubled by the defendants' argument that the words "connected in any capacity with" are subject to indefinite expansion unless confined to consultants, brokers, and other quasi-agents. Persons employed full-time on a project 100 percent of the materials for which (including their own wages) are paid for by a federal agency are "connected in [some] capacity with" that agency as clearly as a broker or consultant would be; we leave to another day decision of the case where the agency pays for only a small fraction of the project costs.

Our interpretation does not place on employees an undue burden of investigating the financial relationships between their employer and the federal agency that funds it. Harris and Gray knew they were stealing the tiles and it is immaterial whether they thought they were committing a federal or merely a state crime in doing so. Culpability does not require proof that the defendant knew the facts that create federal jurisdiction of the offense. See, e.g., United States v. Feola, 420 U.S. 671, 684, 95 S.Ct. 1255, 1263, 43 L.Ed.2d 541 (1975); United States v. Hamilton, 726 F.2d 317, 319-20 (7th Cir. 1984); United States v. Baker, 693 F.2d 183, 186 (D.C. Cir. 1982); United States v. Gregg, 612 F.2d 43, 46-50 (2d Cir. 1979); United States v. Stanford, 589 F.2d 285, 297-98 (7th Cir. 1978); United States v. Herrera, 584 F.2d 1137, 1150 (2d Cir. 1978). This is true even when the penalties under state law for the defendants' conduct are lighter than those under federal law, as they were here. See Ill.Rev.Stat. 1981, ch. 38, ¶¶ 8-2(c), 16-1(e)(1). The argument that federal law can have no incremental deterrent effect unless the potential offender knows that it applies to his conduct is unpersuasive, especially on the facts of this case. The defendants' workplace was festooned with notices of HUD's grants. The defendants must have known that they were working on a project wholly funded by HUD, that the tiles they were stealing had been purchased with HUD funds, and that their misconduct might trigger federal as well as state criminal liability. And the successful prosecution of these defendants will give pause to similarly situated CHA workers. Indeed, the small amount of money involved in their crime suggests that the prosecutions were brought (at great expense to the government) for their demonstration effect, which would be nullified if the statute were read so narrowly that these defendants had to be acquitted. In any event, requiring proof beyond a reasonable doubt of a defendant's knowledge that his conduct is within federal jurisdiction would, by increasing the difficulty of conviction (knowledge always being hard to prove), actually reduce the statute's deterrent effect.

The next question is whether the defendants indeed stole "things of value belonging to" HUD. We do not understand them to be arguing that as soon as federal grant funds are deposited to the grantee's account they cease to "belong to" the granting agency regardless of how much control of the funds the agency retains under the terms of the grant. They could not make that argument after cases like United States v. Hamilton, supra, 726 F.2d at 320; United States v. Montoya, 716 F.2d 1340, 1344 (10th Cir. 1983); United States v. Mitchell, 625 F.2d 158, 161 (7th Cir. 1980); United States v. Smith, 596 F.2d 662, 663-64 (5th Cir. 1979); United States v. Maxwell, 588 F.2d 568, 571-74 (7th Cir. 1978), and especially United States v. Cartwright, 632 F.2d 1290, 1292 (5th Cir. 1980), the last a case under 18 U.S.C. § 657. The CHA had to get HUD's approval for every specific use that it proposed to make of the grant funds, had to maintain and make available to HUD detailed records of expenditures, and had to repay any expenditures that it made and HUD disapproved as well as repay all unexpended funds. The CHA kept the funds in a separate bank account and HUD even negotiated the contract under which the CHA bought the tiles that Harris and Gray stole. The retention of control gave HUD a sufficient interest in the funds to support a prosecution under section 657.

But the defendants argue that once the funds were converted into tangible property (the tiles) to which the CHA held the legal title, HUD no longer had a sufficient interest. We however find it difficult to understand why if the funds remained "things of value belonging to" HUD even after they were paid over to the CHA it should make a difference whether they were kept in a bank account or converted into tangible property. The reference in the statute to "things of value," when read in context ("any moneys, funds, credits, securities or other things of value belonging to such institution, or pledged or otherwise intrusted to its care"), suggests that the form of the property is indeed unimportant. Although it might seem that the tiles, being less liquid than the funds that the CHA used to buy them with, would be less likely to be stolen and hence less needful of the protection of federal criminal law, this consideration is balanced by the fact that building materials sitting on a building site are easier to embezzle than money sitting in a CHA bank account. The narrow interpretation of the statute for which the defendants contend would merely encourage the aspiring embezzler to wait till the grant money was expended pursuant to the terms of the grant.

Our conclusion would be different if the money could not be traced to the particular piece of property that the defendants embezzled, as might be the case if the money was used to buy a can of paint to repaint a chair that had not been bought with federal money, and the defendants then stole the chair. "[W]hen an outright grant is paid over to the end recipient, utilized, commingled or otherwise loses its identity, the money in the grant ceases to be federal." United States v. Smith, supra, 596 F.2d at 664 (dictum). But there is no tracing problem in this case; the defendants embezzled goods that had been bought 100 percent with federal money. So we need not decide whether commingling would necessarily defeat federal criminal liability. Commingling of federal with nonfederal cash would not. See United States v. Gibbs, 704 F.2d 464, 466 (9th Cir. 1983) (per curiam), and cases cited there.

Although we have concluded (postponing an evidentiary question relating to Gray) that the defendants violated section 657, we must consider their argument that the value of the tiles was not proved beyond a reasonable doubt to exceed $100, as required for a felony rather than misdemeanor violation of section 657. If they had been full of new tiles the six boxes would have been worth a shade — but only a shade — over $100. And probably they were full of new tiles. But with all due deference to the contrary view of the experienced district judge we think it apparent that the government failed to prove this fact beyond a reasonable doubt. Before the defendants began to lay the tiles, Matthews, the only witness to their contents, saw five closed boxes and one open one; and he did not look in any of the boxes. If (when the defendants took the boxes) the open box had been missing even a small fraction of its tiles, or if any of the other boxes had been missing even a few tiles, or if some of the boxes had contained old rather than new tiles, the total value of the six boxes would have been less than $100. The cumulative possibilities create a reasonable doubt as a matter of law. The defendants should therefore have been acquitted of the section 657 felony charge and convicted only of misdemeanor violations of the statute.

This raises the question whether the defendants could nevertheless be convicted (as they were) of felony violations of 18 U.S.C. § 371, the general federal conspiracy statute. There is no doubt that there was a conspiracy to violate section 657, and such a conspiracy violates section 371; but there is considerable doubt whether the conspiracy was one to commit a felony violation of section 657. It may have been, despite our conclusion that the evidence does not justify conviction of a completed felony. If the conspiracy was to embezzle as much tile as necessary to do the job and more than $100 worth of tile might have been required for it, the conspiracy would have been one to commit a felony, though in the event only a misdemeanor was committed. See United States v. Shively, 715 F.2d 260, 266-67 (7th Cir. 1983), and cases cited there. Or if the conspiracy was to commit a series of thefts of tile of which the theft of the six boxes for the pretended Matthews townhouse was only the first, it might be possible to view the conspiracy as one to engage in a continuing course of conduct amounting to a felony violation of section 657. Cf. United States v. Billingslea, 603 F.2d 515, 518-20 (5th Cir. 1979). But although there was evidence to support both of these characterizations of the conspiracy we are not clear that there was enough evidence to establish them beyond a reasonable doubt or even that the trier of fact thought there was enough evidence.

But this is unimportant. The defendants were guilty of a conspiracy to defraud an agency of the United States, an independent basis of felony liability under section 371 and one they were charged with in the indictment. Many federal offenses, including many offenses under section 657 and cognate statutes, are not directed against the United States. For example, embezzlement from a federally insured savings and loan association is not, at least if the embezzlement does not endanger the association's solvency and thereby create a risk that the federal agency which insures its deposits will have to make good depositors' losses. As to such offenses the only basis for charging a violation of section 371 is that the defendants conspired to violate a specific federal criminal statute. But the conspiracy in this case was directed against an agency of the United States. A conspiracy to embezzle property belonging to the United States is a conspiracy to defraud the United States ("To conspire to defraud the United States means primarily to cheat the government out of property or money," Hammerschmidt v. United States, 265 U.S. 182, 188, 44 S.Ct. 511, 512, 68 L.Ed. 968 (1924)); and it is a felony regardless of the value of the property taken.

It is true that if the indictment had charged the defendants with just a conspiracy to violate section 657 they could not have been convicted of a felony. It is only because it also charged a conspiracy to defraud the United States that they could be. And since the offense defined in section 657 is more specific than the offense of defrauding the United States (so that conspiracy to violate section 657 is also more specific than conspiracy to defraud the United States), it might seem to follow that the defendants' felony conspiracy convictions violate the principle that when the same conduct is forbidden by two statutes the offender must be punished under the more specific. See, e.g., Busic v. United States, 446 U.S. 398, 406, 100 S.Ct. 1747, 1754, 64 L.Ed.2d 381 (1980). But the conduct forbidden by section 657 and by section 371 (insofar as it punishes conspiracies to defraud the United States) is not the same conduct, though there is an overlap. Section 657 does not require that the defrauded entity be a federal agency, and it would not be surprising if federal criminal law imposed heavier penalties for offenses that hit the federal government in its pocket than for those that merely hit private entities with which the federal government has a relationship as insurer or otherwise. As a matter of fact, the general statute that punishes fraud against the United States or its agencies, 18 U.S.C. § 1001, makes such fraud punishable as a felony regardless of the amount of money involved. Since a minor fraud against the United States is felonious, there is no inconsistency in interpreting section 371 to make a conspiracy to commit such a fraud also felonious.

Moreover, since there is no doubt that what the defendants did here was to defraud an agency of the United States, the interpretation that they argue for could lead the government in future such cases to indict only under the general fraud provision of section 371. If that had been done here the defendants presumably would have tried to show that their conduct also constituted a misdemeanor violation of section 657 — and the trier of fact would have had to decide the defendants' guilt of an offense they had not been charged with in order to decide whether they had committed a felony or a misdemeanor under section 371. An interpretation of section 371 that requires such digressions is not attractive.

Two evidentiary questions are also raised. The first is whether certain statements made by Harris were admissible against Gray as a coconspirator's statements in furtherance of the conspiracy. The first statement, and the only one problematical enough to require discussion, was Spencer's to Agent Matthews at their first meeting. Gray points out that the statement was made before he joined the conspiracy. But the conspiracy was in embryonic existence between Spencer and Harris when Spencer referred Matthews to Harris to do a job that was intended to be a fraud on the federal government. The fact that Gray joined the conspiracy later is of no moment. Statements made in furtherance of a conspiracy are admissible against members of the conspiracy who join after the statements were made, provided the conspiracy was in existence when they were made. United States v. United States Gypsum Co., 333 U.S. 364, 393, 68 S.Ct. 525, 541, 92 L.Ed. 746 (1947).

Gray also argues that there was not enough evidence to convict him beyond a reasonable doubt of conspiracy to defraud the United States, or even of a section 657 misdemeanor. He argues that as a worker on Harris's tile-setting team he was merely following Harris's directions and did not know that he was laying embezzled tile in a private house. But the trier of fact was entitled to disbelieve his story. Gray was present when Harris and Matthews discussed payment for the job. It was Gray who showed Matthews a sample of the tile for Matthews' approval, though, as Gray must have known, if Matthews had been a resident of public housing his approval of the tile would not have been required or sought, because he would not have been the owner of the townhouse — the Chicago Housing Authority would have been. Nor would Gray have given a resident of public housing the two boxes that were not used. And Gray accepted payment in cash from Harris after Matthews paid Harris $260 the day after the job was done, though he could not have believed that the CHA was paying him in this manner. We need not decide what Gray's criminal liability would be if his only connection to the conspiracy between Harris and Spencer had been accepting payment knowing it was for unauthorized work; there was, as we have just seen, a good deal more evidence of his participation in the embezzlement and the conspiracy.

Since the defendants should not have been convicted of felony violations of section 657, the convictions and sentences imposed for those violations must be set aside and the case remanded for resentencing of the defendants for misdemeanor violations of that statute. See Tinder v. United States, 345 U.S. 565, 569-70, 73 S.Ct. 911, 913-14, 97 L.Ed. 1250 (1953). Although we affirm the conspiracy convictions and although the district judge imposed concurrent sentences on the section 657 and conspiracy counts, we shall remand for resentencing on the conspiracy count as well. The judge's exercise of his sentencing discretion might have been influenced by his erroneous belief that each of the defendants had committed two felonies rather than, as we have found, one felony (under section 371) and one misdemeanor (under section 657). United States v. Shively, supra, 715 F.2d at 269.

SO ORDERED.