Before HIGGINBOTHAM, COSTA, and OLDHAM, Circuit Judges. ANDREW S. OLDHAM, Circuit Judge: The question presented is “Where’s the beef?” Wendy’s Kind of Commercial, BROADCASTING, Mar. 26, 1984, at 57. Stewart Kile Williams pleaded guilty to four counts of wire fraud for purporting to broker cattle deals worth millions of dollars, pocketing the money, and then disappearing the herd. The district court ordered more than $2 million in restitution. Williams challenges that award on the ground that the Government failed to prove which cattle he sold and which he stole. We affirm. I. A. For three years, Williams brokered cattle sales between Jones Alto Colorado Ranch and Wyatt Ranches of Texas. Wyatt Ranch bought the cattle. Jones Ranch sold them. And Jones Ranch paid Williams one third of its profits from the sales. The transactions began in late 2015. The first sale went off without a hitch. A few months later, in January of 2016, Williams made a second sale to Wyatt Ranch. This sale did not go as smoothly as the first order, but Wyatt Ranch received the cattle. So far, so good. In March of 2016, Williams made a third sale to Wyatt Ranch. Wyatt Ranch purchased black cows. But when the cows arrived, Wyatt Ranch was dissatisfied. Not only were they delivered late, they had “problems.” Some were the wrong color, some were barren and had no udders, and some were sick or had died. Wyatt Ranch said no dice; it returned the defective cattle. Bradford Wyatt, the administrator of Wyatt Ranch, complained to Williams and threatened to sue Jones Ranch based on the defective cattle. Williams made excuses and persuaded Wyatt Ranch not to sue by promising to provide additional cattle to make up for Wyatt Ranch’s losses. Williams eventually finalized the purchase, and he even threw in an extra $30,000 worth of cattle. But Bradford Wyatt remained dissatisfied and decided Wyatt Ranch was “done with Williams.” Williams, however, wasn’t done with Wyatt Ranch. Though Bradford Wyatt stopped ordering cattle, Williams didn’t tell that to Jones Ranch. Instead, Williams pretended to be Bradford Wyatt. Williams got a new phone number and an email address ([email protected]) and gave them to Jones Ranch. Then Williams used his fake identity to purchase more cattle from Jones Ranch. Williams forged Bradford Wyatt’s signature on purchase orders. And when Jones Ranch attempted to contact Wyatt Ranch personnel, Williams responded—pretending to be Bradford Wyatt. Under the pretense that “Bradford Wyatt” could not afford to prepay Jones Ranch for the cattle, Williams convinced Jones Ranch to front almost $2,000,000 to facilitate the sales. Jones Ranch paid some of that money to Williams directly; it paid some to various other ranches to purchase cattle for “Bradford Wyatt”; and it paid some to facilitate the storage, transportation, and feed of cattle that Williams fraudulently ordered. Jones Ranch’s losses included: December 8, 2015: Jones Ranch transferred $105,000 to Williams; February 2, 2016: Jones Ranch transferred $61,224 to Williams (including $25,244 for a feed mixer); March 21, 2016: Jones Ranch transferred $285,000 to Williams; April 18, 2016: Jones Ranch transferred $85,200 to Jordan Cattle Auction; May 12, 2016: Jones Ranch transferred $601,150 to Williams; July 25, 2016: Jones Ranch transferred $303,000 to Williams; September 7, 2016: Jones Ranch transferred $369,175 to Jordan Cattle Auction; March 24, 2017: Jones Ranch transferred $143,500 to Maddux Cattle Co.; July 18, 2017: Jones Ranch issued a cashier’s check in the amount of $185,000 to Cross M. Cattle; and August 24, 2017: Jones Ranch issued a cashier’s check in the amount of $58,500 to Williams’s company, Casa Cattle. Although Jones Ranch made these transfers to Williams and other entities, “Bradford Wyatt” missed several payments. So Jones Ranch sought a promissory note and security agreement to protect itself. Williams signed the promissory note and security agreement—again doing so under the false pretense of being Bradford Wyatt. Eventually, Jones Ranch contacted Wyatt Ranch about its failure to pay. Bradford Wyatt was confused—he hadn’t authorized an order or received any cattle since March of 2016. Jones Ranch called the number Williams had provided. When Williams answered, he pretended to be Bradford Wyatt. But upon learning that the real Bradford Wyatt was on the line, Williams confessed. B. A grand jury charged Williams with four counts of wire fraud in violation of 18 U.S.C. § 1343 and one count of aggravated identity theft in violation of 18 U.S.C. § 1028A(a)(1). Williams pleaded guilty to the wire-fraud counts. Under his plea agreement, Williams waived his right to appeal.* In exchange, the Government dropped the aggravated-identity-theft charge. The principal dispute at sentencing was how to quantify the losses Williams imposed on his victims. To determine the custodial sentence, the district court turned to the U.S. Sentencing Guidelines. Under those Guidelines, the offense level for wire fraud is based on the greater of the actual or intended loss. See U.S.S.G. § 2B1.1 cmt. n.3(A). Using that definition of the loss amount, the Pre-Sentence Report (“PSR”) recommended an offense level of 25:
