OPINION
HAWKINS, Circuit Judge
In these consolidated appeals, we must determine whether a presumption of validity attaches to a stipulation
by defense counsel that their clients waive their right to a jury trial on their criminal charges. Defendants Kevin Laney and Brian Federico contend that: (1) the stipulations submitted by'their respective trial counsel did not effectively waive their Sixth Amendment rights and (2) their convictions on several counts of conspiracy and mail fraud are not supported by sufficient evidence. We ' conclude that counsel’s stipulations in this case did not raise a presumption of validity, and the record is insufficient to show that the jury trial waivers were voluntary, knowing, and intelligent. Therefore, although we conclude that the convictions are supported by sufficient evidence, we reverse and remand based on the ineffective jury trial waivers.
I. BACKGROUND
The scheme giving rise to the convictions below arose out of Laney and Federico’s work in the construction and concrete industries. Laney worked as a project manager for Matrix Services, Inc. (“Matrix”), an industrial construction company specializing in construction and repair work in the energy. industry. Federico worked as a manager of the concrete company Imperial Shotcrete (“Imperial”), which served as a subcontractor on several Matrix projects.
The state presented evidence that, in .approximately 2005, Federico approached Imperial’s owner, Miguel Ibarria, with an arrangement that would allow Ibarria, Federico, Laney, and other Matrix project managers to make additional money from Matrix projects. Under the arrangement, Federico would provide Ibarria with the specifications for a job, and Ibarria would provide a quote consisting of the project expenses and Imperial’s standard markup. Federico would then talk to the assigned Matrix project' manager, who would inform Federico when there was “more room” in the budget for concrete work. Federico would then come back to Ibarria with another, higher bid . suggestion that Imperial would in turn submit to Matrix- as its bid on the project. That new inflated bid generally corresponded to Matrix’s internal budget ceiling for concrete work. The Matrix project manager would approve the bid and award the job to Imperial, Imperial would complete the concrete work and bill Matrix “for whatever number they ... told [Ibarria] to make the proposal for.” Federico would provide Ibarria with “some extra wording” to include on the invoices to Matrix. The Matrix project manager involved would approve the invoice, and Matrix would pay Imperial.
After Matrix paid Imperial, Imperial would receive an invoice from a fictitious company, in fact fabricated by the involved Matrix project managers, purporting to charge for work associated with the project. These invpices were entirely false and described materials not used or services not performed. Federico would supply the project manager -with the amount to include on the false invoice, and the project manager would submit that invoice to Imperial, Once the project manager received a check from Imperial, he would deposit the money in his own account and write a cheek back to Federico for his agreed-upon share of the money. ¡
The scheme continued for several years, involved several projects, and ultimately resulted in Laney and Federico receiving hundreds of thousands of dollars through these fictitious entities. In 2010, Matrix, suspecting a potential financial fraud within the company, launched an internal investigation and vendor audit of Imperial. The amount of the fraud ultimately uncovered was approximately $1.6 million.
II. PROCEDURAL HISTORY
An investigation by the Federal Bureau of Investigation (“FBI”) soon followed Matrix’s internal- investigation. The FBI .-investigation led to the indictment of Lahey, Federico, Ibarria, and two other Matrix project managers, Brandon Hourmouzus and Charles Burnette, on multiple counts of mail fraud and conspiracy to commit mdil fraud.
A. The Indictment
The Grand Jury charged Ibarria, Federico, Laney, Hourmouzus, and Burnette with “defraud[ing] Matrix by knowingly submitting or causing to be submitted, false and inflated invoices to Matrix that exceeded the actual work performed and the materials used.” It charged that La-ney, Federico, Hourmouzus, and Burnette “submitted false invoices in the names of legitimate existing businesses ■ and in the names of businesses created specifically for the purpose of-perpetuating the fraud on Matrix.” Additionally, “Ibarria marked up the false invoices received by Imperial from the co-defendants for the businesses and passed the inflated invoices onto Matrix knowing that they were fraudulent. Matrix paid the invoices submitted by Imperial and Ibarria in turn paid the appropriate co-defendants after taking Ibarria’s mark-up as personal profit.” '
In relevant part, Count One charged Ibarria, Federico, Laney, Hourmouzus, 'and Burnette with “knowingly con'spir[ing] to defraud Matrix by submitting fraudulent invoices for materials used and work performed by the businesses knowing that the materials had not been used and the work had not been performed.” Count Two charged Ibarria, Federico, and Laney with mail fraud in connection with a $90,000 check from -Matrix made payable and mailed to Imperial related to a project to repair two tanks in McKittrick, California for Plains All-American (the “McKittrick Project”). Count Three charged Ibarria, Federico, and Hourmouzus with mail fraud •in connection with a $46,645 check.from Matrix made payable and mailed to Imperial related to a project in Eureka, California (the “Eureka Project”).
Ibarria, Hourmouzus, and Burnette pled guilty to Count One, and the government agreed to dismiss the individual mail fraud counts charged against them. Laney and Federico entered pleas of not guilty and proceeded to trial.
B. Jury Trial Waivers
On March 25, 2015, the court accepted a stipulation waiving Laney’s right to a jury trial. The stipulation stated that “[t]he parties [had] held a conference call with the Court” several days earlier and “informed the Court that [] the defendant and the government waive their right.to a jury trial and jointly request to proceed with trial before the Court.” The stipulation also addressed counsel’s scheduling conflict and an agreement as to the admissibility of the government’s business records, bank records, public records, and evidence summaries. The stipulation contained only counsel’s electronic signature, and the docket indicates that it was filed by the government. The record does not indicate that Laney was present at the telephonic hearing preceding this stipulation.
Several days later, the court held another telephonic conference. Federico and La-ney were represented by counsel at the conference but did not personally appear. The court minutes state: “A stipulation as to Defendant Federico waiving Jury Trial to be submitted. Counsel, requested a Bench Trial as to both Defendant Federico and Defendant Laney The parties subsequently submitted and the court accepted a stipulation waiving Federico’s right to- a jury trial and requesting a joint bench trial. The stipulation, which the government filed, again' contains only the prosecution and defense counsel’s electronic signatures and sets forth other pre-trial agreements regarding documentary evidence and trial scheduling. The stipulation also explains that proceeding with a bench trial would allow for the introduction of pre-trial statements to law enforcement officers, which implicated all the defendants and could not be introduced in a jury trial if made by a non-testifying co-defendant. See Bruton v. United States, 391 U.S. 123, 135-37, 88 S.Ct. 1620, 20 L.Ed.2d 476 (1968). Thus, by submitting to a bench trial, Federico and Laney could have a joint trial.
C. The Trial and Convictions
In the eleven-day bench trial, the government called multiple witnesses including Ibarria, Hourmouzus, Burnette, the individual who performed Matrix’s audit, and the lead FBI case agent. Federico and Laney also testified during the trial. After the conclusion of trial, the district court made findings of facts and conclusions of law, finding Laney guilty on Counts One and Two and Federico guilty on Counts One, Two, and Three. The district court sentenced Laney and Federico to sixty and seventy months in prison, respectively. La-ney and Federico timely appealed challenging the validity of the jury trial waivers and the sufficiency of the evidence.
III. STANDARD OF REVIEW
We review de novo the adequacy of a jury trial waiver, United States v. Shorty, 741 F.3d 961, 965 (9th Cir. 2013). For a challenge to the sufficiency of the evidence following a bench trial, we review “whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” United States v. Atkinson, 990 F.2d 501, 502-03 (9th Cir. 1993) (internal citation and quotation omitted) (emphasis in original).
IV. DISCUSSION
A. Jury Trial Waivers
Laney and Federico contend that their convictions must be vacated because the record does not reflect adequately that they made voluntary, knowing, and intelligent waivers of their rights to a jury trial.
To be valid, a defendant’s waiver of the Sixth Amendment right to a jury trial must be voluntary, knowing, and intelligent. United States v. Christensen, 18 F.3d 822, 824 (9th Cir. 1994). “In most cases, adherence to the dictates of [Federal Rule of Criminal Procedure] 23(a) creates the presumption that the waiver was voluntary, knowing, and intelligent.” United States v. Bishop, 291 F.3d 1100, 1113 (9th Cir. 2002) (citation omitted). That rule provides that where a defendant is entitled to a jury trial “the trial must be by jury unless: (1) the defendant waives a jury trial in writing; (2) the government consents; and (3) the court approves.” Fed. R. Crim. P. 23(a). Although we have “implore[d]” district courts to conduct colloquies with the defendant before accepting a waiver of his or her right to a jury trial, the failure to do so “does not violate either the Constitution nor does it ipso facto require reversal.” United States v. Cochran, 770 F.2d 850, 851, 853 (9th Cir. 1985) (internal citations omitted).
In assessing the effectiveness of the waivers we must determine first whether a written waiver must be signed, or otherwise made, by the defendant personally— as opposed to defense counsel—in order to comply with Rule 23(a) and raise the presumption of validity. Although we have not yet addressed this issue specifically, circuits that have addressed the issue hold that the written waiver contemplated in Rule 23(a)(1) must be executed by the defendant personally; the failure to strictly comply with that requirement, however, does not constitute reversible error if the record otherwise shows that the waiver was voluntary, knowing, and intelligent. United States v. Carmenate, 544 F.3d 105, 109 (2d Cir. 2008); United States v. Leja, 448 F.3d 86, 93-94 (1st Cir. 2006); United States v. Robertson, 45 F.3d 1423, 1432-33 (10th Cir. 1995). The plain language of Rule 23(a), our case law regarding jury trial waivers, and the general presumption against finding a waiver of a constitutional right lead us to the same conclusion.
Rule 23(a) requires “the defendant” to waive his or her right to a jury trial “in writing.” Fed. R. Crim. P. 23(a)(1) (emphasis added). Consistent with the plain language of the rule, we have suggested previously that the written waiver contemplated in Rule 23(a) is one that the defendant personally executes. See United States v. McCurdy, 450 F.2d 282, 283 (9th Cir. 1971) (“Ideally, counsel ... would have called to the attention of the trial judge the provisions of Rule 23, and McCurdy’s signature on the appropriate form would have been obtained.”); see also United States v. Duarte-Higareda, 113 F.3d 1000, 1003 (9th Cir. 1997) (“In Cochran, for example, we held that the district court was not required to question the defendant about his understanding of the jury waiver where the defendant had signed a written waiver in accordance with Fed. R. Crim. P. 23(a).” (citation omitted)). And, in Bishop where we found a written waiver alone sufficient, the written waiver was executed by the defendant personally. See 291 F.3d at 1113-14.
Relatedly, we have permitted oral waivers in lieu of Rule 23’s writing requirement only “where the record clearly reflects that the defendant ‘personally gave express consent in open court, intelligently and knowingly.’ ” United States v. Saadya, 750 F.2d 1419, 1420 (9th Cir. 1985) (quoting United States v. Reyes, 603 F.2d 69, 71 (9th Cir. 1979) (emphasis added)). In crafting this exception, we emphasized the importance of the defendant’s verbal confirmation of the waiver for the record in order to fulfill the purposes of Rule 23. See United States v. Guerrero-Peralta, 446 F.2d 876, 877 (9th Cir. 1971) (explaining that the purpose of the writing requirement “is to provide the best record evidence of the express consent of a defendant” (internal quotation marks omitted)). We have acknowledged previously that “[tjhere is little support for the proposition that [counsel’s] assurances are relevant to the question whether a defendant’s oral waiver is knowing and intelligent.” Shorty, 741 F.3d at 968.
Courts have a “serious and weighty responsibility” to determine whether a waiver is knowing and intelligent, Christensen, 18 F.3d at 826 (quoting Johnson v. Zerbst, 304 U.S. 458, 465, 58 S.Ct. 1019, 82 L.Ed. 1461 (1938)), and we must “indulge every reasonable presumption against waiver of fundamental constitutional rights,” United States v. Gonzalez-Flores, 418 F.3d 1093, 1102 (9th Cir. 2005) (quoting United States v. Hamilton, 391 F.3d 1066, 1071 (9th Cir. 2004)).
Therefore, consistent with the plain language and purpose of Rule 23(a) as well as the holdings of our sister circuits, we hold that the proper practice under Rule 23(a) is for the defendant to personally execute the written waiver; a written stipulation signed by defense counsel alone—like the stipulations at issue in this case—will not raise a presumption of validity. Nevertheless, the absence of a defendant's ■ signature will not constitute reversible error if the record otherwise shows that the defendant’s waiver was voluntary, knowing, and intelligent. See Carmenate, 544 F.3d at 108-10 (affirming based on other indicia of validity in record despite absence of defendant’s signature), United States v. Khan, 461 F.3d 477, 491-92 (4th Cir. 2006) (same); Leja, 448 F.3d at 94-95 (same); cf. Robertson, 45 F.3d at 1432-33 (reversing where only evidence of waiver in record was stipulation signed by defense counsel alone).
We cannot determine from the record before us whether Laney and Federico’s waivers were voluntary, knowing, and intelligent. The'written stipulations were contained in larger pre-trial filings bearing only the electronic signatures of counsel, which the government filed.
The discussions regarding the jury trial waivers occurred exclusively during hearings where Laney and Federico were not present. And, prior to trial, the district court did not address the ^defendants directly about their jury trial waivers, but mentioned only in passing that “this-shouldn’t be too long given that this is not going, to be a jury trial.”
The “requirements of Rule 23 cannot be satisfied by a post-trial reconstruction of the record.” Saadya, 750 F.2d at 1421. Consequently, we reject the contention that certain statements made after the conclusion of trial cure the earlier deficiencies in the record. Cf. Reyes, 603 F.2d at 71-72 (remanding based on ineffective twelve-member jury-waiver despite defendant’s post-trial confirmation that he authorized waiver prior to counsel’s oral stipulation). Essentially, the stipulation here is tantamount to an oral waiver by counsel outside the defendant’s presence, which our precedent deems-insufficient,' Cf id.
Because an invalid jury waiver is structural error, we reverse and remand. See Shorty, 741 F.3d at 969.
B. Sufficiency of the Evidence
Federico and Laney contend that the evidence was insufficient to support each count of conviction. Because a challenge to the sufficiency of the evidence implicates a defendant’s rights under the Fifth Amendment’s Double Jeopardy Clause, we must address Laney and Federico’s contentions that there was insufficient evidence to sustain their convictions despite our holding regarding their jury trial waivers'.
United States v. Bailon-Santana, 429 F.3d 1258, 1262 (9th Cir. 2005). We will not set aside a conviction for insufficient evidence “if, viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the elements of the crime proved beyond a reasonable doubt.” Id. (quoting United States v. Boulware, 384 F.3d 794, 810 (9th Cir. 2004)).
a. Count One: Conspiracy
Laney and Federico contend that there was insufficient trial evidence to support their convictions under Count One because the conspiracy shown at trial did not involve all individuals charged in the Indictment; To prove a conspiracy, the government was required to show “an agreement between two or more persons to accomplish an illegal objective, coupled with one or more overt acts in furtherance of the illegal purpose.” United States v. Hubbard, 96 F.3d 1223, 1226 (9th Cir. 1996). The agreement may be inferred from circumstantial evidence. Id,
“A single conspiracy may involve several 'subagreements dr subgroups of conspirators.” United States v. Bibbero, 749 F.2d 581, 587 (9th Cir. 1984) (citation omitted). “Typically, the inference of an overall agreement is drawn from proof of a single objective ... or from proof that the key participants and the method of operation remained constant throughout the conspiracy.” United States v. Duran, 189 F.3d 1071, 1080 (9th Cir. 1999) (citations omitted). Other relevant factors include: “the nature of the scheme; the identity of the participants; the quality, frequency, and duration of each conspirator’s transactions; and the commonality of time and goals.” Bibbero, 749 F.2d at 587 (citation omitted).
A reasonable trier of fact could conclude from the evidence presented at trial that, at a minimum, Laney, Federico, Hour-mouzus, and Ibarria engaged in a single conspiracy. Although arguing now that he intended to defraud Imperial rather than Matrix, Federico testified that Laney and Hourmouzus were the Matrix project managers who were in on his “plan.” Ibarria confirmed during his testimony that Federico presented a scheme .to him that involved Laney and Hourmouzus, He further testified to the overall scheme and common method .by which he and Federico worked with Laney and Hourmouzus to inflate Imperial’s bids and share in the excess profits,from Matrix. The government also elicited testimony demonstrating that Laney and Hourmouzus worked with Federico and-Ibarria to carry out a common scheme contemporaneously and with the-same means. . ...
Even assuming the evidence was insufficient to show that Burnette participated in the conspiracy with Federico and Laney, it would not be grounds for reversal. As Laney and Federico concede, Ibar-ria and Burnette continued the scheme in later projects, demonstrating, at most a second conspiracy. Although “[t]he issue of whether a single conspiracy has been proved is a question of the sufficiency of the evidence,” the issue becomes one of variance where the evidence at trial tends to show the existence of two conspiracies rather than one ongoing conspiracy as alleged in the indictment. Duran, 189 F.3d at 1078, 1080-81 (citing Bibbero, 749 F.2d at 586). The district court did not rely on those projects in its findings regarding Laney and Federico, and Laney and Federico have not demonstrated any prejudice stemming from a variance regarding Bur-nette’s participation. See id. at 1081-83.
b. Count Two: Mail Fraud Involving the .McKittrick Project
Laney also ■ contends that there was insufficient evidénce to sustain his conviction under Count Two where the government was required to prove under 18 U.S.C. § 1341: “(1) ... a scheme to defraud, (2) using or causing the use of the mails to further the fraudulent scheme, and (3) specific intent to defraud.” See United States v. Rogers, 321 F.3d 1226, 1229 (9th Cir. 2003).
Conceding that he fraudulently obtained money stemming from Matrix’s payment to Imperial for the McKittrick Project, Laney contends that his fraudulent scheme did not induce Matrix to place the $90,000 check in the mail, but instead occurred after Matrix had already mailed the check. Contrary to Laney’s contentions, a rational trier of fact could have found that he was involved in inflating Imperial’s bid and causing Matrix to mail Imperial the inflated check for the McKittrick Project. Indeed, Matrix project manager Khary Sands testified at trial that Laney was the initial project manager on the McKittrick Project; by the time Sands took over as project manager, Imperial had been engaged as the concrete subcontractor for the project, and its bid already had been approved. To Sands, the already-approved bid seemed higher than expected. When the scope of the project expanded at Federico’s urging after Laney had transferred to another location, the cost of the project simply was doubled based on the original bid.
Imperial invoiced Matrix for its exact bid amount of $90,000. And, Laney invoiced Imperial for $70,000 worth of materials purportedly used in the McKittrick Project, which he did not supply. In the overall scheme, the Matrix project manager involved in inflating the bid amount was the individual from whom Ibarria expected to receive an invoice when the project had been completed and Matrix had paid Imperial. And, the McKittrick Project was one of the projects for which Ibarria expected to receive an invoice from the Matrix project manager.
Although Laney and Federico testified that Laney had no involvement in the McKittrick Project, a rational trier of fact could have properly disbelieved such testimony. See Duran, 189 F.3d at 1079. Thus, viewing the evidence in the light most favorable to the prosecution, a rational trier of fact could have found the elements of mail fraud beyond a reasonable doubt. See Bailon-Santana, 429 F.3d at 1262.
c. Intent to Deceive Matrix
Finally, Federico contends that there was insufficient evidence that he acted with the specific intent to defraud Matrix.
To commit the crime of mail fraud, the defendant must act with specific intent to defraud. See United States v. Green, 745 F.2d 1205, 1207 (9th Cir. 1984). “The government satisfies the requirement of proof of specific intent ... if it proves the existence of a scheme which was reasonably calculated to deceive persons of ordinary prudence and comprehension, and this intention is shown by examining the scheme itself.” Id. (internal quotation marks and citation omitted).
Looking at the Eureka Project charged in Count Three as an example, the evidence established the following: Ibarria’s initial bid for the project was $16,000. Hourmouzus informed Federico that there was “more room” in the budget, and at Federico’s direction, Imperial submitted a bid for $47,000. Many other subcontractors on the project came in significantly under budget, allowing Matrix or the customer to realize that amount as profit or savings, respectively. Imperial performed the contracted work and invoiced Matrix for $46,645. The invoice was slightly under budget in order to avoid raising red flags. After Matrix paid Imperial, Hourmouzus submitted false invoices to Imperial for $30,000—the difference between Ibarria’s initial bid and the ultimate invoice to Matrix. Imperial paid Hourmouzus’s invoice, and Hourmouzus and Federico shared the profits.
Viewing this evidence in the light most favorable to the prosecution, a rational trier of fact could have found the element of specific intent beyond a reasonable doubt. See Bailon-Santana, 429 F.3d at 1262.
V. CONCLUSION
Although the defendants’ convictions were supported by sufficient evidence, the record does not establish that Laney and Federico’s jury trial waivers were voluntary, knowing, and intelligent. Accordingly, we must reverse and remand.
REVERSED and REMANDED.