Chung Lo, a San Francisco real estate broker, appeals her conviction for eight counts of mail fraud in violation of 18 U.S.C. § 1341 and for related offenses. Lo maintains, as to some of the mail fraud counts, that the government failed to present sufficient evidence to prove that a mailing occurred and, as to others, that the government failed to prove sufficiently that the mailings were in furtherance of the alleged fraudulent scheme. She also claims that the statute of limitations barred a superseding indictment filed by the government and that in any case, the two conspiracy charges were improperly pled. Finally, Lo contends that the district court’s refusal to allow broader cross-examination of a government witness prejudiced her defense. While four of Lo’s sufficiency-of-the-evidence arguments have merit, the remainder of her claims do not. We therefore reverse Lo’s conviction on four mail fraud counts and affirm as to the rest of the case.

I. Background

The charges against Lo all stem from a series of four real estate transactions she oversaw in the early 1990s, all of which were both byzantine and indubitably fraudulent. We begin here by providing a brief overview of the four transactions, leaving recitation of some of the factual details for later.

The first transaction originated in the spring of 1990 when Aristela Wise and her husband Arthur came to Lo for assistance in buying a home. Although the Wises had little money for a down payment, Lo encouraged them to fill out a loan application and soon called them with information about a house for sale on Sarazen Avenue in Oakland, California (“Sarazen property”). Lo knew the seller of the house, Frank Rosario, having helped him buy and sell property in the past, and she set out to conclude a deal with the Wises. Although the high cost of the house concerned them, Lo assured the Wises that the seller was willing to make accommodations and that a deal could be reached.

The details of the transaction — like the details of all of these transactions — are complicated, but the essence is this: Lo told the Wises that they would not qualify for a loan on their own credit-worthiness alone, and suggested instead that they include an investor named “Wong K. Chow” — whose existence is dubious — as co-signer on their application. The proposed deal would obligate the Wises to pay Chow $3000 for his services while Chow would in turn quitclaim his interest in the home back to the Wises after the deeds were recorded and the sale finalized. The Wises agreed to the proposal, and Lo prepared a loan application which she submitted to Imperial Bank (“Imperial”). The application contained numerous false statements about the Wises’ employment, earnings and assets and about Chow’s intentions as a co-borrower.

Imperial accepted the application, funded the loan for over $280,000, and paid Lo a broker’s fee. The sale of the Sarazen property closed in July 1990, and the deeds were recorded and mailed thereafter. The Wises eventually defaulted on the loan.

The next two transactions involved a pair of sham real estate sales Lo orchestrated in 1991. Her client, Jayson Bryant, owned two separate properties in Oakland, California, one at 9515 MacArthur Boulevard (“MacArthur property”) and one at 2738 79th Avenue (“79th Avenue property”). Both properties were heavily leveraged. In order to avoid foreclosure, Bryant sought refinancing. Lo arranged a fraudulent refinancing scheme, whereby Bryant would “sell” the properties to his wife, Elma Bryant, using her maiden name, Aglibot, and a straw purchaser, Frank Bosnich. Once again, Lo submitted loan applications containing assorted false information, this time to California Mortgage Services (“CMS”) for the MacArthur property, and to Beverly Hills Security Company (“BHSC”) for the 79th Avenue property. Both loan applications were approved. A third investor, Edward Brubaker, also loaned money against the MacArthur property.

After the “sales” closed, the Alameda County Recorder’s office mailed the original grant deeds to Aglibot and Bosnich, the original deeds of trust to CMS and BHSC, and, some time later, a grant deed from Elma Aglibot to Jayson Bryant. Eighteen months afer the sale, Bosnich assigned his interest in the properties to Aglibot, and the County Recorder’s office sent the corresponding deed to her. The Bryants eventually defaulted on both loans.

The fourth transaction involved the attempted sale of a property on Hugo Street in San Francisco (“Hugo property”) in 1991. Rosalina Bautista approached Lo, seeking assistance in buying a home. Although she did not believe she had enough money to buy a house alone, she indicated that her brother, Roland Bautista, and sister, Jocelyn Bautista Panaligan, would be able to help. Lo asked all three to complete loan application forms. Based on the information provided, Lo advised Rosalina that neither Roland nor Jocelyn’s income was sufficient to qualify for financing but assured her that she would make other arrangements to secure a loan. Lo then prepared new loan applications which she submitted to Greater Suburban Mortgage (“GSM”) for the purchase of the Hugo property. The new applications contained numerous false statements about the Bau-tistas’ financial circumstances. This time, the lending institution discovered the fraud in its review of the application and notified Lo that it would not grant the loan.

In June 1996, the government filed an initial fourteen count indictment charging Lo, inter aha, with mail fraud and conspiracy to commit mail fraud. It filed a superseding thirteen count indictment in July 1998. After the government dropped one of the charges, a jury convicted Lo of the remaining twelve coun+s and this appeal followed.

II. Discussion

A. The Hugo Property Mail Fraud

We begin our analysis with Count Thirteen of the superseding indictment, charging Lo with mail fraud in connection with the Hugo property purchase.

Mail fraud includes two general elements: first, the government must prove that a defendant devised or intended to devise a scheme to defraud a victim of his money or property; second, it must prove that in executing the scheme, the defendant made use of or caused the use of the mails. See United States v. Sayakhom, 186 F.3d 928, 941 (9th Cir.1999). There was more than sufficient evidence to prove that the scheme was fraudulent, and Lo does not contend otherwise. Instead, she asserts that there was insufficient evidence to make out the second element, maintaining that the government’s evidence was not adequate to prove she used the mail to carry out the alleged fraudulent scheme. This sufficiency-of-the-evidence challenge can succeed only if, viewing the evidence in the light most favorable to the prosecution, no rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt. See Jackson v. Virginia, 443 U.S. 307, 319 , 99 S.Ct. 2781 , 61 L.Ed.2d 560 (1979); United States v. Deeb, 175 F.3d 1163, 1168 (9th Cir.1999). Applying this standard, we conclude that the government’s evidence on the Hugo property mail fraud is so scant as to be insufficient to support the conviction.

The only mailing allegation in Count Thirteen of the indictment is that Lo knowingly caused the mailing of a “Truth in Lending Disclosure/Good Faith Estimate” document (the “Truth in Lending” document) as part of the scheme to secure a fraudulent loan. A Truth in Lending document lists all fees a borrower will incur when obtaining a loan. The law requires loaning institutions to provide the document to borrowers.

To establish the mailing element, the government offered testimony by a loan processor and an operations manager at GSM about the bank’s procedures for gen erating a Truth in Lending document in the course of a normal loan application. The GSM witnesses explained that when the mortgage company receives an application, it generates the document and, within three days from receipt of the application, sends it to the borrower. The GSM witnesses also testified that because the law requires this document, GSM has a series of provisions in place to insure that it is mailed, including cross-checks by other loan departments.

The foregoing is the sum total of the mailing testimony produced on the Hugo property count. No copy of the Truth in Lending notice in question was introduced at trial. No GSM witness testified that he or anyone else at the company had ever seen the specific, critical document, that there was any record that it had ever existed, that it was ever in GSM’s loan files (whether at the time of trial or earlier) or that the loan file was ever complete. Moreover, although the Bautistas, the putative borrowers, also testified at trial, they did not state that they had ever received the document, and they, also, did not produce a copy of it.

The government contends that the custom and practice evidence alone was enough to prove the mailing beyond a reasonable doubt, maintaining that the jury could have inferred that since GSM processed the loan, GSM must have created and sent the document. So the question is whether on the custom and practice evidence alone, and with the gaps in testimony from witnesses who should have been able to testify to the document’s existence, any rational juror could have concluded beyond a reasonable doubt both that the document had in fact been generated and that it had been mailed.

The government argues that a rational juror could have so concluded, relying on cases such as United States v. Brackenridge, 590 F.2d 810 (9th Cir.1979), and United States v. Green, 745 F.2d 1205 (9th Cir.1984), which held that direct proof of mailing is not always required. In Brack-enridge, for example, the question was whether initials of a bank’s bank-by-mail department employee on a fraudulent check were adequate to demonstrate that the check had been received in the mail, where there was also testimony suggesting that in the “routine custom and practice” for handling cross-country withdrawal requests at the bank, a mailing would result. Brackenridge, 590 F.2d at 811 . The court held that this was “adequate circumstantial evidence to support the inference that the check cashed by appellant in this case was mailed,” adding that “[djirect proof of mailing was not required.” Id. In Green , similarly, the court determined that evidence that a document was placed in an outgoing basket, combined with testimony by an employee that it was routine practice to collect items in such baskets and place them in the United States mail, was sufficient to support a § 1341 conviction. Green, 745 F.2d at 1208 .

In Brackenridge and Green , the document could have been waylaid before the mail went out so that it never reached the post office. But absent any evidence that it was so misdirected, and in light of common experience, the jurors were entitled to conclude, beyond a reasonable doubt, that the internal mailing system into which the particular document was introduced terminated as it ordinarily does with an actual mailing.

Here, however, the chain of inferences required to conclude that the Truth in Lending document was mailed is much longer than in Brackenridge and Green . The jurors here had to infer the very existence of the document, and also had to infer that the document, if produced, was in fact introduced into the system GSM used for bringing mail to the post office, not lost or misdirected before it got to any individual or equipment involved in the mailing process. Only then would the fairly minor inference involved in Bracken-ridge and Green — that a document that was introduced into the mailing depart ment or equipment was in fact mailed-arise.

Obviously, as the chain of inferences based on usual practices gets longer, the probability that nothing went wrong in administering those practices lessens. At some point, a reasonable doubt arises concerning whether, as Murphy’s Law predicts, that which can go wrong did go wrong. The chain of inferences from the evidence necessary in this case to conclude that mailing occurred extends well beyond that point., See United States v. Burks, 867 F.2d 795, 797 (3d Cir.1989), rev’d on other grounds, United States v. Hannigan, 27 F.3d 890 (3d Cir.1994) (custom and practice evidence is insufficient in a mail fraud case where the evidence contains no “specific reference to the mailing in question,” because, absent direct evidence regarding the mailing of the specific document, “the circumstances [do not] ... support the inference and exclude all reasonable doubt to the extent of overcoming the presumption of innocence”) (quoting United States v. Brooks, 748 F.2d 1199, 1203 (7th Cir.1984)).

Additionally, in the business context, where the question is whether a document that did exist and did reach its destination was in fact mailed rather than arriving in some other manner, some small measure of custom and practice evidence is likely to be a necessary link in the chain of mailing evidence. Clerical personnel often will not be able to testify directly to precisely what documents were in fact placed in the United States Postal Service box. So, in those circumstances, there is no plausible negative inference to be drawn from the absence of more direct evidence. In contrast, business organizations ordinarily do keep copies or records of critical documents, particularly legally required documents. Yet, in this case the absence of any direct evidence of the document’s existence was not explained at trial. There is, consequently, a strong negative inference to be drawn here from the nature of the evidence produced that would be inappropriate where the custom and practice evidence is limited to matters as to which direct evidence is unlikely to be available.

Because “[t]he federal mail fraud statute does not purport to reach all frauds, but only those limited instances in which the use of the mails is a part of the execution of the fraud, leaving all other cases to be dealt with by appropriate state law,” Kann v. United States, 323 U.S. 88, 95 , 65 S.Ct. 148 , 89 L.Ed. 88 (1944), there is reason to be scrupulous in reviewing the evidence to assure that the mailing element is adequately proven. As in all criminal cases, in undertaking sufficiency of the evidence review the paramount concern is assuring that the jury abided by the beyond-a-reasonable-doubt standard. In mail fraud cases, there is the real danger that the mailing issue will seem much less important to the jury than whether a fraud was perpetuated. Yet, the mailing is, of course, an essential element of the crime, and is the gatekeeper for separating those cases that are the exclusive province of the states from those that may be tried in federal court under the mail fraud statute. To accept attenuated circumstantial facts of the kind presented here as sufficient to meet the mailing element would, as a practical matter, eradicate the significance of the distinctive consideration that governs which fraud crimes may be prosecuted in the federal judicial system and which are to remain solely state matters.

We therefore conclude that in this case the evidence of the required mailing is far too tenuous to be sufficient, and reverse Lo’s conviction on Count Thirteen accordingly.

B. The Remaining Mail Fraud Counts

Counts Four through Seven, concerning the sale of the MacArthur property, and Nine through Eleven, concerning the sale of the 79th Avenue property, also charge Lo with mail fraud in violation of 18 U.S.C. § 1341 . The mailings alleged in these counts were mailings by the County Recorder’s office of grant deeds and deeds of trust for the two properties. These mailings occurred after the loans had been funded and after the deeds had been recorded in the Recorder’s office. The specific deeds mailed by the Recorder’s office, as alleged in these counts, were: with regard to both properties, a deed of trust in favor of the lender, mailed to the lender shortly after the transaction closed, and a grant deed from Frank Bosnich to Elma Aglibot, mailed about a year and a half after the original transaction; with regard to the MacArthur property, a grant deed from Jayson Bryant to Elma Aglibot and Frank Bosnich, mailed to them but returned as undeliverable shortly after the transaction closed, and a deed of trust in favor of Edward Brubaker, mailed over a month after the transaction closed; and as to the 79th Avenue property, a grant deed from Elma Aglibot to Jayson Bryant, mailed around three months after the transaction closed.

Lo does not dispute that the County Recorder mailed deeds to the lenders and to the owners, real and sham, of the two Oakland properties. Rather, Lo contends that the MacArthur and 79th Avenue deed mailings cannot support her conviction under § 1341 because there was insufficient evidence that the mailings were “essential” to the alleged fraudulent scheme and were therefore part of the scheme’s execution.

To prevail in a prosecution under § 1341, the government must establish that a defendant used the mails “for the purpose of executing such [fraudulent] scheme or artifice or attempting to do so.” 18 U.S.C. § 1341 . The required connection between the mailing and the scheme is not, however, as close as Lo suggests. Although a mailing must occur in the execution of the scheme — that is, as a “step in [the] plot,” Schmuck v. United States, 489 U.S. 705, 711 , 109 S.Ct. 1443 , 103 L.Ed.2d 734 (1989) (quoting Badders v. United States, 240 U.S. 391, 394 , 36 S.Ct. 367 , 60 L.Ed. 706 (1916)) — the mailing need not be an essential element of the scheme. Rather, it is sufficient if the mailing is “incident to an essential part of the scheme.” Pereira v. United States, 347 U.S. 1, 8 , 74 S.Ct. 358 , 98 L.Ed. 435 (1954) (emphasis added).

Stressing the fact that all the mailings of deeds occurred after the loan transaction was funded, the deeds were recorded, and Lo was paid her fee, Lo maintains that the fraudulent scheme was completed by the time any of the deeds were mailed. The general principle upon which Lo relies is correct, for the government may not prevail without demonstrating that the mailings were incident to the execution of the scheme, rather than part of an after-the-fact transaction that, although foreseeable, was not in furtherance of the defendant’s fraudulent scheme. See, e.g., United States v. Maze, 414 U.S. 395, 400-02 , 94 S.Ct. 645 , 38 L.Ed.2d 603 (1974); Parr v. United States, 363 U.S. 370, 393 , 80 S.Ct. 1171 , 4 L.Ed.2d 1277 (1960); Kann, 323 U.S. at 95 , 65 S.Ct. 148 ; United States v. Manarite, 44 F.3d 1407, 1412-13 (9th Cir.1995).

But the issue is not one purely of time sequence. “[Subsequent mailings can in some circumstances provide the basis for an indictment under the mail fraud statutes,” United States v. Sampson, 371 U.S. 75, 80 , 83 S.Ct. 173 , 9 L.Ed.2d 136 (1962), so the pertinent question is not whether or not the defendant “had obtained all the money [she] expected to get” before the mailing occurred, id. at 79 , 83 S.Ct. 173 . Rather, as in Sampson and Schmuck , the mailing can occur after the defendant has obtained her fee, if “the mailing is part of the execution of the scheme as conceived by the perpetrator at the time.” Schmuck, 489 U.S. at 715 , 109 S.Ct. 1443 ; see also Sampson, 371 U.S. at 80 , 83 S.Ct. 173 .

For purposes of applying these principles, the most similar case in this court is United States v. Miller, 676 F.2d 359 (9th Cir.1982), in which, as here, the defen dants were engaged in a fraudulent refinancing scheme. To avoid creditors, homeowners deeded their homes to the defendant’s company, which in turn found “straw purchasers” to complete loan applications and buy the properties. The straw purchasers then deeded the homes back to the original owners. At each step, the deeds were recorded and returned by mail. This court held that although the loans had been issued before the time of the mailings, the mailings still satisfied the requirements of the mail fraud statute, noting that “[a] fraudulent scheme may depend on a mailing even after the defrauders have received their money.” Miller, 676 F.2d at 362 (citing United States v. Galloway, 664 F.2d 161 , 163 n. 3 (7th Cir.1981)). The court added that in that case, “[e]ven after [the defendant] took his ‘fee,’ his scheme required the straw purchaser to deed that property back to the homeowner. Only then was the transaction complete.” Id.

Here, as in Miller , the scheme as originally conceived by the appellant was not completed once the loan went through and she received her fee. Lo’s plan was structured to make it appear that the properties had been sold, when in fact the sales were a sham. The jury could have found that the routine mailings of the deeds to the owner of the property interest was incidental to an essential aspect of this overall sham sale scheme. The mailings could serve to “lull the victims” — in this case, the loaning banks — “into a false sense of security, postpone their ultimate complaint to the authorities, and therefore make the apprehension of the defendants less likely,” by assuring them that the conveyance of the property had gone forward in accordance with the usual procedures of the Recorder’s office and providing them with documentary proof thereof. Maze, 414 U.S. at 403 , 94 S.Ct. 645 ; see also Manarite, 44 F.3d at 1412-13 (“Lulling schemes can include mailings sent by someone other than the defrauder, even routine mailings in the ordinary course of business.”). The situation, then, is entirely different than in cases such as Kann, Parr, Maze, and Manarite , in which the after-the-payoff mailing, far from furthering the defendant’s scheme, was likely to unravel it. See Manarite, 44 F.3d at 1413 (sham credit transaction likely to be discovered when the creditor processed the false credit application through the mail); Maze, 414 U.S. at 403 , 94 S.Ct. 645 (fraudulent use of credit card likely to be discovered when defrauded creditors mailed in their credit card receipts).

From the foregoing analysis we conclude that there was sufficient evidence to sustain the convictions on Counts Four, Five and Nine, the counts alleging mailing of a grant deed attesting to one of the original sham “sales,” and of the deeds of trust.

With respect to Counts Seven, Ten and Eleven, Lo makes a slightly different argument, contending that the transfers from Bosnich to Aglibot and Aglibot to Bryant were simply unrelated to the effort to secure the fraudulent loans.

Bosnich played a limited but important role in the MacArthur transaction. By listing him as a co-purchaser Lo was able to use the relative strength of his credit rating to secure loans for AglibotBryant. In return for the risk of being listed on the mortgage for the MacArthur property, Bosnich was paid $1500. He testified that he was not expected to contribute any money toward the mortgage payments and that after a year he planned to quitclaim his interest in the property back to the Bryants.

Bosnich did not, however, quitclaim his interest in the MacArthur property a year later, but did so only after another several months, after the FBI approached him with questions about the fraudulent loan applications and informed him that his name was listed on the 79th Avenue property. Lo contends that the jury could only have reasonably found that the transfer of the MacArthur property from Bosnich to Aglibot-Bryant was unrelated to any fraudulent loan scheme but was triggered instead by the FBI investigation. There is, however, sufficient evidence of a prior understanding that Bosnich would quitclaim the MacArthur deed back to the Bryants to permit the jury properly to find that the transfer of the MacArthur property to AgliboN-Bryant was part of the execution of Lo’s original plan, whether the precise timing was influenced by the FBI investigation or not. We thus affirm Lo’s conviction as to Count Seven.

As to the 79th Avenue property, however, the evidence is considerably flimsier. Both Bosnich and Aglibot-Bryant denied knowing that their names were on the 79th Avenue property. Neither they nor anyone else testified to a prior plan to deed back that property. Indeed, Bosnich and Aglibot-Bryant could hardly have agreed to deed back a property with which they did not know they had any connection. Nor is there any evidence that Lo ever told, or intended to tell, Bosnich or Agli-bot-Bryant that she had used their names on the 79th Avenue property loan. This being the state of the evidence, no reasonable juror could conclude beyond a reasonable doubt that it was part of Lo’s fraudulent plan that Bosnich or Aglibot-Bryant would deed back the 79th Avenue property. We therefore reverse the convictions as to Counts Ten and Eleven.

Finally, with respect to Count Six, Lo also claims that the loan from Brubaker was unrelated to the overall scheme. This contention, it appears, is correct. Brubaker was among the original creditors of the MacArthur property. The sham sale scheme allowed Bryant to pay off that initial obligation. In order to enhance Aglibot-Bryant’s loan application, however, Lo sought to inflate Aglibot-Bryant’s assets. To this end, money from Brubaker was placed in an account in Aglibot-Bryant’s name. Brubaker was then repaid out of the escrow account before the MacArthur transaction closed. No mailings are charged with respect to that transaction.

It appears that Brubaker subsequently made a second loan to the Bryants which he secured with a deed of rents on the MacArthur property and which led to the mailing at issue in Count Six. There is no basis in the evidence, however, for concluding that this second loan was part of Lo’s fraudulent scheme. We therefore find that there was insufficient evidence to support Lo’s conviction on Count Six.

C. The Statute of Limitations

Challenging again her convictions on Counts Four through Seven and Nine through Eleven, Lo next argues that the statute of limitations barred the charges in the superseding indictment. Failure to comply with the statute of limitations, however, is an affirmative defense which the defendant waives if not raised at trial. See United States v. LeMaux, 994 F.2d 684, 689-90 (9th Cir.1993). Lo points to this court’s recent decision in United States v. Fuchs, 218 F.3d 957 (9th Cir.2000), to suggest that this issue should be reviewed at least for plain error. We do not find Fuchs applicable, however, because there the defendant raised both a pre-trial objection and a challenge at trial claiming that the charges against him were untimely. Id. at 961 . In this case, since Lo raised the argument for the first time on appeal, we find it waived and need not address it.

D. Adequacy of Indictment

Counts Eight and Twelve charge Lo with conspiracy to commit mail fraud in violation of 18 U.S.C. § 371 . In Pereira , the Supreme Court observed that the use of the mails element of mail fraud can be satisfied if the defendant acts with “knowledge that the use of the mails will follow in the ordinary course of business, or where such use can reasonably be foreseen, even though not actually intended.” Pereira, 347 U.S. at 8-9 , 74 S.Ct. 358 . Lo contends that because the government did not allege this mental state element in Counts Eight or Twelve, the indictment was defective as to those two counts

In general, we review the sufficiency of an indictment de novo. See United States v. Neill, 166 F.3d 943, 947 (9th Cir.), cert. denied, 526 U.S. 1153 , 119 S.Ct. 2037 , 143 L.Ed.2d 1046 (1999). Lo did not, however, raise this sufficiency argument until this appeal, nor does she claim that she was in any way prejudiced in preparing and presenting her defense because of the manner in which the substantive offense element of the conspiracy counts was alleged.

Failure of an indictment to state an offense is never waived, it is true. But we have recognized that a late challenge “suggests a purely tactical motivation” and is needlessly wasteful because pleading defects can usually be readily cured through a superseding indictment before trial. United States v. Pheaster, 544 F.2d 353, 360 (9th Cir.1976). Additionally, “the fact of the delay tends to negate the possibility of prejudice in the preparation of the defense,” because one can expect that the challenge would have come earlier were there any real confusion about the elements of the crime charged. Id. at 360, 363 . For all these reasons, “indictments which are tardily challenged are liberally construed in favor of validity.” Echavarria-Olarte v. Reno, 35 F.3d 395, 397 (9th Cir.1994) (quoting United States v. Rodriguez-Ramirez, 777 F.2d 454, 459 (9th Cir.1985)). The question, then, is whether read in a common sense, nontechnical fashion, the indictment adequately set forth the conspiracy counts.

Counts Eight and Twelve allege the elements of the crime of conspiracy but, as to the substantive crime the conspirators allegedly conspired to violate, there is nothing but a bare citation to § 1341, the mail fraud statute. None of the overt acts alleged in either conspiracy count state that the act was accomplished through use of the mails. The government contends that because these counts charge conspiracy, however, not mail fraud, the indictment, liberally read, is sufficient.

The Supreme Court held many years ago that as long as the conspiracy itself is adequately alleged, a conspiracy indictment need not allege the offense that is the object of the conspiracy with the same precision as would be necessary where that offense is itself the crime charged. See Wong Tai v. United States, 273 U.S. 77, 81 , 47 S.Ct. 300 , 71 L.Ed. 545 (1927); see also Pheaster, 544 F.2d at 360 ; Stein v. United States, 313 F.2d 518, 520 (1962). Even under the forgiving Wong Tai standard, a conspiracy allegation that omitted any explication whatever of the offense that is the object of the conspiracy other than a citation to the United States Code could well be fatally defective, if challenged in a timely manner. Where as here, however, there was no timely challenge, indeed no challenge at all until appeal, the requisite liberal reading of the indictment should take into account fair inferences from the indictment as a whole. See Echavarria-Olarte, 35 F.3d at 397 .

Counts Four through Seven allege with particularity substantive mail fraud counts with regard to the MacArthur property, and Counts Nine through Eleven allege with particularity substantive mail fraud counts with regard to the 79th Avenue property. Count Eight adds a corresponding allegation of conspiracy regarding the MacArthur property, and Count Twelve adds a corresponding conspiracy allegation regarding the 79th Avenue property. The overt acts alleged in Counts Eight and Twelve are substantially the same as the paragraphs in Counts Four through Seven and Nine through Eleven spelling out the fraudulent scheme for purposes of the substantive mail fraud counts. The fair inference is that the mail fraud offenses that were the object of the conspiracies in Counts Eight and Twelve were the substantive mail fraud schemes alleged in the respective, immediately preceding, parallel substantive counts. That is almost certainly what the grand jury intended and what the parties understood throughout the proceedings in the district court, and it is demonstrably what the judge thought when she instructed the jury that the offense that was the object of each of the conspiracy charges was “mail fraud as charged in the indictment.” With that inference, the enunciation of the conspiracy counts is sufficient to serve both the prior notice and the avoidance of double jeopardy purposes served by adequately-pleaded indictments. See Pheaster, 544 F.2d at 354 .

We conclude that the indictment adequately alleged the conspiracy counts and affirm the corresponding convictions.

E. Limitation of Cross-Examination

Lo’s final challenge is to the district court’s limitation of cross-examination of a government witness. At trial, the government presented Rosario, the seller of the Sarazen property, to testify about his role in the transaction. On cross-examination, Lo’s attorney wanted to pursue a line of questions suggesting that Rosario had engaged in fraudulent dealings of his own in connection with a bankruptcy, in order to prove that Rosario had a motive to dissemble regarding Lo’s role and his own role in the sale. The district court found these allegations too speculative, however, and excluded them under Federal Rule of Evidence 408. Lo contends that this limitation violated her Sixth Amendment confrontation clause rights and that her conviction on Counts One and Two relating to the Sarazen sale should be reversed.

The Supreme Court has emphasized the policy favoring expansive witness cross-examination in criminal trials. See Olden v. Kentucky, 488 U.S. 227, 231 , 109 S.Ct. 480 , 102 L.Ed.2d 513 (1988); Davis v. Alaska, 415 U.S. 308, 316 , 94 S.Ct. 1105 , 39 L.Ed.2d 347 (1974). Similarly, this court has observed that “[f]ull disclosure of all relevant information concerning [adverse witnesses’] past record and activities through cross-examination and otherwise is indisputably in the interests of justice.” United States v. Brooke, 4 F.3d 1480, 1489 (9th Cir.1993). The confrontation clause, however, does not guarantee unbounded scope in cross-examination. See Delaware v. Van Arsdall, 475 U.S. 673, 679 , 106 S.Ct. 1431 , 89 L.Ed.2d 674 (1986) (“The Confrontation Clause guarantees an opportunity for effective cross-examination, not cross-examination that is effective in whatever way, and to whatever extent, the defense might wish.” (quoting Delaware v. Fensterer, 474 U.S. 15, 20 , 106 S.Ct. 292 , 88 L.Ed.2d 15 (1985))). Rather, we review a trial court’s decision to limit the scope of cross-examination for abuse of discretion, and will find a Confrontation Clause violation only if the trial court’s ruling “ ‘limits relevant testimony[,] ... prejudices the defendant’ ... and denies the jury ‘sufficient information to appraise the biases and motivations of the witness.’ ” United States v. Bensimon, 172 F.3d 1121, 1128 (9th Cir.1999) (internal citations omitted).

The trial judge here was well within her discretion in limiting the cross-examination as she did. She permitted full exploration of the impact of Rosario’s impending di vorce and bankruptcy filings on his motivations and interests. Lo succeeded through cross-examination in demonstrating that at the time of sale, Rosario was highly motivated to sell the property because he was concerned about his impending divorce and bankruptcy proceedings and was about to lose his job. That testimony certainly allowed the jury to judge whether Rosario was unusually anxious to conclude the sale of his home.

The further cross-examination which the trial judge refused to permit concerned evidence that purportedly showed that the divorce and bankruptcy were fraudulent, and that Rosario might have himself committed the offenses with which Lo was charged. There was no allegation of fraud during the course of the bankruptcy proceedings, the evidence of bankruptcy fraud on which Lo sought to rely was exceedingly thin, and the documentary evidence linking Lo to the transaction was strong. Given the highly speculative nature of Lo’s fraud allegations, we find that the district court did not abuse its discretion by limiting cross-examination of Rosario. Lo’s conviction on these two counts is affirmed.

III. Conclusion

For the foregoing reasons, we affirm Lo’s conviction on Counts One and Two, Four and Five, Seven through Nine, and Twelve. Because we find that the government failed to provide sufficient evidence to establish the required mailing element with regard to the Hugo property, we reverse her conviction for mail fraud under Count Thirteen. Also, because we find insufficient evidence linking Lo to the Bru-baker charges or to Aglibot-Bryant’s transfer of the 79th Avenue property back to her husband and Bosnich’s transfer of the same .property to Aglibot-Bryant, we reverse her convictions for mail fraud under Counts Six, Ten and Eleven as well. This matter is hereby remanded to the district court for further proceedings consistent with this opinion. AFFIRMED in part, REVERSED in part, and REMANDED.

. Although Lo used his name on both loan applications, Bosnich was evidently only told about the MacArthur property. He did not learn that he was listed as a co-owner of the 79th Avenue property as well until FBI agents investigating the scheme approached him. . See United States v. Serang, 156 F.3d 910, 914 (9th Cir.1998) (noting that "if the government shows that a defendant knows or can reasonably foresee that use of the mails will follow in the ordinary course of business, 'then he causes the mails to be used' ”) (internal citations omitted). . That Lo did not herself specifically plan the mailing is immaterial. In her Reply Brief, appellant notes that she has “never suggested that she could not have predicted the mails ultimately might be used in connection with the loans she helped obtain for her clients." And indeed, Lo must have known that the mailing of the deeds would occur. Printed at the top of the recording documents were specific instructions to the Recorder to mail the deed to the appropriate party when recorded. So the mailings were an expected, ordinary “incident" of the recording process, completing the process by notifying the interested parties that it had occurred and providing them with proof that it had. An experienced broker would certainly — or so the jury could conclude — know that. . There is no challenge to the jury instructions.