ESCHBACH, Circuit Judge.

In this criminal appeal, we are asked to decide whether the admission of the confession of a non-testifying co-defendant violated the appellant’s right under the Sixth Amendment to cross-examine the witnesses against him. We are also asked to determine the sufficiency of the evidence against the appellant. Because the admission of the confession violated the appellant’s right of confrontation, we reverse his conviction on Count II and remand that count to the district court for a new trial. We affirm Key’s convictions on Counts III, IV, V, and VII, and remand those counts for resentenc-ing.

A seven-count mail fraud indictment was returned against the appellant, Willie J. Key, and three co-defendants. The indictment charged the defendants with using the mails to defraud insurance companies by submitting false claims, in violation of 18 U.S.C. § 2 and 18 U.S.C. § 1341. Key’s involvement in the scheme was alleged to have taken three forms. First, he was charged with having submitted false receipts in connection with claims for losses allegedly incurred during burglaries at his home (Counts IV, V, and VI). Second, he allegedly supplied fraudulent receipts to two of his co-defendants, who then submitted the receipts as proof of burglary losses (Counts III and VII). Finally, he was charged with falsely representing to an insurer that he had been injured in an automobile accident (Count II). Count I was dismissed before trial.

Before trial, Key filed a motion in limine which requested, among other things, that the government be prohibited from introducing a confession made by Key’s co-defendant, Michael Baker. Relying on the government’s representation that all references to Key in the confession would be avoided, the trial judge denied Key’s motion. Key was tried jointly with Baker and another defendant, Anthony Madison, before a jury. He was convicted on Counts II, III, IV, V, and VII, and acquitted on Count VI. Key was sentenced to five four-year terms, to be served concurrently.

II.

A. The Confession

In presenting the evidence relating to Count II, the government relied on a letter sent by an attorney to an insurance company to establish the mailing. The letter notified the insurer that Key and another co-defendant, Anthony Madison, had sustained injuries as the result of an automobile accident involving cars driven by Baker, the policy holder, and Key. Anthony Madison claimed to be a passenger in Key’s car at the time of the accident. In order to show that the letter was in furtherance of a fraudulent scheme, the government sought to establish that the accident referred to in the letter never occurred.

The government made its case through the testimony of several witnesses. A police officer testified that on February 23, 1980, he had received a report of an automobile accident. During the course of an on-the-scene investigation, the officer questioned Baker and Key, who told him that they were the drivers of the cars involved. The officer testified that he neither saw nor spoke to Madison. An attorney testified that he had sent a letter to Baker’s insurance company, informing it that Key and Madison had sustained injuries in the accident. The claims representative for the insurer testified that he contacted Key in the course of his investigation of the claim because “he was the driver that our policy holder ran into.” The government’s final *1126 witness was Robert Ridgeway, a postal inspector. Ridgeway testified that Baker admitted to him that “the accident which allegedly occurred on February 23,1980, never actually occurred. It was not an accident.” 1 Baker did not take the stand.

Key testified in his own behalf. While denying that he had authorized the attorney to represent him, Key testified that he did go to the attorney’s office, and maintained that the accident had occurred. Key’s doctor also testified that he had treated Key for injuries soon after the accident supposedly happened.

Key contends that under the rule of Bruton v. United States, 391 U.S. 123, 88 S.Ct. 1620, 20 L.Ed.2d 476 (1968), the admission of Baker’s out-of-court confession violated Key’s constitutional right of confrontation under the Sixth Amendment. In Bruton, the Supreme Court held that, in the context of joint trials, the admission of the confession of a non-testifying co-defendant that inculpates another defendant on trial violates the Confrontation Clause. Since the non-testifying co-defendant is unavailable for cross-examination, the weight to be accorded “powerfully incriminating extrajudicial statements of a co-defendant who stands accused side by side with the defendant” cannot be tested. Id. at 126, 88 S.Ct. at 1622. If such a confession is otherwise admissible, it may be admitted under some circumstances if all references to a co-defendant are deleted. United States v. English, 501 F.2d 1254 (7th Cir.1974), cert. denied sub nom. Hubbard v. United States, 419 U.S. 1114, 95 S.Ct. 791, 42 L.Ed.2d 811 (1975). However, “[t]he introduction of a confession from which the names of co-defendants have been excised may violate the Bruton rule if in context the statement is clearly inculpatory of a co-defendant and vitally important to the Government’s case.” English v. United States, 620 F.2d 150, 152 (7th Cir.), cert. denied, 449 U.S. 859, 101 S.Ct. 160, 66 L.Ed.2d 75 (1980); see also United States v. Gonzalez, 555 F.2d 308, 316 (2d Cir.1977) (exception to Bruton rule where jury must make substantial inference to identify co-defendant as person mentioned in statement, and evidence, even if incriminating, not vital part of government’s case).

In the instant case, Baker’s confession both directly incriminated Key and formed a crucial part of the government’s proof under Count II. There was no dispute that Key and Baker reported an accident to the police. Nor did Key dispute that he and Baker told the police officer they were the drivers of the cars involved. Baker’s admission that the accident was staged, then, was the equivalent of a statement that Key was lying. As such, it directly implicated Key.

Further, the confession was vital to the government’s proof of fraud because it was the only evidence before the jury that the accident was staged. The situation before us is thus distinguishable from United States v. Madison, 689 F.2d 1300 (7th Cir. 1982), where we found no Bruton violation. In that case, the appellant, Madison, complained of a co-defendant’s statement that revealed that “somebody else” involved in the kidnapping had a gun. Madison, however, was identified by the kidnap victim, as well as by other eyewitnesses. Further, the government established through the testimony of the victim that Madison had a gun. The confession, therefore, added little to the government’s case against Madison. Cf. United States v. Gonzalez, 555 F.2d 308 (2d Cir.1977) (Bruton violation where incriminating inference compelled and only other evidence against defendant circumstantial).

As we noted above, the appellant objected to the government’s proposed use of Baker’s out-of-court statement through a pre-trial motion in limine. Key should have repeated his objection during trial when it became apparent that, contrary to the government’s assertions, Ridgeway’s testimony was going to implicate Key. Had the appellant done so, we are confident that the *1127 able trial judge in this case (who raised the question of a possible Bruton problem sua sponte twice before trial) would have prevented the error. Nevertheless, the admission affected Key’s substantial right to confront his accusers, and was plain error. Fed.R.Crim.Pro. 52(b); United States v. Taylor, 374 F.2d 753 (7th Cir.1967). Key’s conviction under Count II must therefore be reversed and the case remanded for a new trial on that count.

In determining the effect of the erroneous admission of the confession on Key’s convictions on the other counts, we are mindful that, in order to sustain the convictions, we must be convinced “beyond a reasonable doubt that the error complained of did not contribute to the verdicts] obtained.” Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 828, 17 L.Ed.2d 705 (1967). We believe from our examination of the record as a whole, and in light of Key’s acquittal on Count VI, that the jury gave individual consideration to each of the charges against Key. We therefore conclude beyond a reasonable doubt that the violation of the Bruton rule did not influence the jury’s verdicts on the other counts in the indictment.

B. Sufficiency of the Evidence

At the close of the government’s evidence, and again at the end of trial, Key moved unsuccessfully for a judgment of acquittal. In testing the trial court’s denial of the motion, we must ask “whether, after reviewing the evidence in the light most favorable to the government, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979) (emphasis in original).

Key contends that without the erroneously admitted confession, insufficient evidence remains to sustain his conviction under Count II. Presumably, Key is arguing not only that this court should reverse this conviction, but also that Double Jeopardy should attach to the reversal. While we agree that Key’s conviction on Count II must be reversed because of the erroneous admission of the confession, we will not excise from the record evidence found inadmissible for trial error, and then assess the remaining evidence for sufficiency. See United States v. Tranowski, 702 F.2d 668 (7th Cir.1983); Linam v. Griffin, 685 F.2d 369 (10th Cir.), cert. denied, — U.S. —, 103 S.Ct. 1207, 75 L.Ed.2d 447 (1982); United States v. Sarmiento-Perez, 667 F.2d 1239 (5th Cir.), cert. denied, 459 U.S. 834, 103 S.Ct. 77, 74 L.Ed.2d 75 (1982).

Key also argues that the government failed to establish- his intent to defraud the insurance companies. We do not agree. Key was charged with submitting receipts he knew to be false to substantiate burglary losses. He was also charged with providing such receipts to others, who used them in a similar manner. In Counts III, IV, and VII, the government relied on the submission of receipts from General Paddlers, Inc., a company for which Key claimed he sold stereos on a commission basis. 2 The government presented evidence that the company was not located at the address listed on the receipts and did not have a license to do business in Illinois — in short, that the company did not exist. In Count V, the government presented testimony that Key had submitted a receipt to his insurer to substantiate the loss óf a television he claimed to have purchased from Ernie Martin’s T.V. and Appliances in the K-Mart South Shopping Center. He claimed to have bought the television three or four months before the burglary. Ernie Martin then testified that the receipt for the television did not come from his store, which, in fact, had moved from the K-Mart South location over a year prior to the time Key claimed to have made the purchase. The evidence was sufficient for the jury to conclude that Key intended to defraud the insurance companies.

Finally, Key argues that the government failed to show that the mailing upon which it relied in Count III — the initial insurance application of co-defendant Sam *1128 uel Gray — was in furtherance of a scheme to defraud. 3 In determining the relationship between the use of the mails and the fraudulent scheme in a mail fraud case, our inquiry concerns whether the use of the mails that is charged in the indictment and shown by the evidence may properly have been said to be for the purpose of executing the scheme. United States v. Craig, 573 F.2d 455 (7th Cir.), cert. denied, 439 U.S. 820, 99 S.Ct. 83, 58 L.Ed.2d 110 (1977). The question, then, is whether a rational jury could have found that Gray’s application was in furtherance of a scheme to defraud.

The evidence showed that Gray applied for insurance covering his personal belongings on August 10, 1979. Early in the morning of August 18, 1979, Gray reported a burglary to the police. Some time thereafter, but within a month, Gray submitted a proof of loss form which contained fraudulent receipts, obtained from Key. The government also presented evidence showing that the defendants in this case reported five other burglaries to the police after obtaining insurance. With the exception of one of these alleged burglaries, the longest period of time that elapsed between the initial application for insurance and the subsequent report of a burglary was one month. 4 “The jury is permitted to infer from one fact the existence of another essential to guilt, if reason and experience support the inference.” Tot v. United States, 319 U.S. 463, 467, 63 S.Ct. 1241, 1244, 87 L.Ed. 1519 (1943). Here, the fact that the alleged burglary occurred only a week after Gray obtained insurance, coupled with a similar pattern of fraud used by the other members of the scheme, would support the rational inference that Gray applied for insurance for the purpose of executing the scheme. As a member of the mail fraud scheme, Key is responsible for mailings caused by another member of the scheme. United States v. Joyce, 499 F.2d 9 (7th Cir.), cert. denied, 419 U.S. 1031, 95 S.Ct. 512, 42 L.Ed.2d 306 (1974). We therefore conclude that a rational trier of fact could have found that the mailing was in furtherance of the scheme to defraud.

III.

For the reasons expressed above, Key’s convictions on Counts III, IV, V, and VII are affirmed. Key’s conviction on Count II is reversed, and the case is remanded to the district court for a new trial on Count II. In light of our disposition of Count II, we also remand Key’s convictions under Counts III, IV, V, and VII to the district court for resentencing. In so doing, we do not intimate that the district court is required to reduce the sentences.

. As Key did not dispute that the accident had been reported as the government claimed, and that he had admitted being the driver of one of the cars, Key’s attorney did not cross-examine the government’s witnesses.

. In Count IV, Key himself submitted the receipts. The receipts in Counts III and VII were submitted by other defendants, who obtained them from Key.

. Gray was tried separately and convicted.

. The government’s evidence showed the following:

Defendant and Date of Date Burglary Count Application Reported

Baker, Count II Dec. 3, 1979 Dec. 12, 1979

Gray, Count III Aug. 10, 1979 Aug. 18, 1979

Key, Count IV Oct. 15, 1979 Nov. 20, 1979

Key, Count V Same July 14, 1980

Key, Count VI Oct. 17, 1980 Oct. 21, 1980

Madison, Count VII Jan. 28, 1980 Feb. 10, 1980