PER CURIAM.

Kim Tae Sung was convicted of selling imitation hair care products with counterfeit trademarks, in violation of 18 U.S.C. § 2320(a). Last year we affirmed this conviction but remanded for resentencing. 51 F.3d 92 (7th Cir.1995). The district court treated Kim as responsible for $960,000 of counterfeit goods, on the theory that he had purchased 20,000 cartons, enough to hold 240,000 bottles, at a retail price of $4 per bottle. Yet the record shows that Kim actually filled no more than 17,600 bottles, placing an upper bound of $70,400 on infringing sales, and lacked supplies essential to continue the operation. After working through the Sentencing Guidelines, we set out these legal rules to govern the resentencing:

[U.S.S.G] § 2B5.3 tells the court to impose a sentence based on the retail value of infringing products; § 2F1.1 does not answer the question whether the infringing boxes should be treated as if they represented the retail value of the completed product or only the value of the boxes themselves; to answer that question one visits § 2X1.1 and learns that everything depends on how close the defendant came to completing additional crimes. By purchasing the boxes, Kim took a step toward the sale of 240,000 counterfeit bottles. That attempt is enough to count the retail value of the whole 240,000 bottles, if intent to sell 240,000 bottles has been established with “reasonable certainty”, subject to a deduction of 3 levels under § 2X1.1(b)(1) unless Kim “was about to complete all [necessary] acts but for apprehension”. It is not clear to us that “but for apprehension” Kim had any hope of reaping a million dollars from counterfeit hair products, but the district court should make the essential inquiries in the first instance.

51 F.3d at 95-96 (emphasis in original). Two questions had to be addressed on remand: first, whether the evidence establishes “with reasonable certainty” that Kim intended to sell 240,000 bottles of bogus products; second, whether Kim “was about to complete all *196 [necessary] acts but for apprehension”. The first inquiry is subjective, the second objective.

Although these instructions were explicit, the district judge soon informed counsel: “I don’t understand why this case has come back to me.” The judge disagreed with our interpretation of the Guidelines and announced: “[I]f the law is as I believe it is,-I don’t see any reason to do anything other than explain myself [better].” Remand ensued, the judge suggested, not from any error in the sentence but from this court’s shortcomings. “I think that we have a misunderstanding here and I’m not sure that whatever law clerk upstairs first looked at this file gave it the kind of reading that we gave it in advance....... There are things in that [presentence] report that if whoever gave the first review of this matter upstairs read the report carefully and with understanding of what went on down here, and if they had ever conducted a criminal trial, they might have noted.” There is much more in the same vein. Despite the prosecutor’s concession that Kim is entitled to a three-level reduction under § 2X1.1(b)(1), the district judge refused to reduce the offense level and proceeded to impose the same 48-month sentence — which we again vacate.

The district court found that Kim wanted to sell as much fake product as he could, to make as much profit as possible, and that he was not one to waste money. Supplemented on remand, the record shows that cartons could be purchased in lots of 1,000, with price decreasing as lot size increases. This supports an inference that Kim hoped to use all of the cartons; otherwise he was squandering money. But was a plan to sell 240,000 bottles established “with reasonable certainty”? This is a higher standard than the preponderance rule that ordinarily governs at sentencing. Usually we assume that judges know and follow the law on burdens of persuasion, but the district judge’s remarks on remand call that assumption into question. The judge stated: “Does there have to be a finding of reasonable certainty? Is there any place ever in any of the books anyplace that I have to declare reasonable certainty when the record itself demonstrates reasonable certainty?” The answers are yes and yes. There must be such a finding, if only because our opinion requires it. The decision of a higher court controls whether the lower tribunal agrees or not. Appellate review is not an exercise in persuasion. And that standard is not our invention. The “place in the books” that establishes a reasonable-certainty standard is U.S.S.G. § 2X1.1(a), which the district judge neither quoted nor discussed. The district judge’s wonderment at this rule, and the implication that he need not use it because it does not “appear in the common law as a determinative factor for a trier of fact”, leads us to conclude that the findings of fact are unreliable. Kim may have planned to sell 240,000 bottles originally but changed his mind before ordering lesser quantities of the other inputs. Only an explicit finding that the Guidelines’ standard has been met will suffice.

As for the potential three-level reduction: the district court made no finding at all. The court stated that it would not reduce the offense level but did not say why. We infer that the judge believed that Kim’s intent to sell as much of the counterfeit product as he could is dispositive on this question. Our opinion held otherwise. Unless Kim “was about to complete all [necessary] acts but for apprehension”, § 2X1.1(b)(1), a three-level reduction is obligatory. Intent to sell more is a necessary but not a sufficient condition. We know that Kim lacked the materials to fill more than 17,600 bottles. The record suggests that during the four months preceding his apprehension, Kim had neither sold any counterfeit hair care products nor ordered the materials necessary to manufacture more. Kim had not only the law but also the market to contend with. His initial customers were displeased with the product’s quality; their complaints set off both private and public investigation. Any finding that Kim was just about to fill and sell another 222,400 bottles when he was nabbed would be clearly erroneous.

Kim must be resenteneed, again. His final offense level, after all adjustments, cannot exceed 20, and his sentence cannot exceed 41 months’ imprisonment. The offense level *197 can be as high as 20 only if an intent to sell 240,000 bottles of counterfeit product has been established “with reasonable certainty.” We remand so that the district judge may at last address that question and impose a lawful sentence. If the district judge expresses or implies unwillingness to follow these instructions, Kim should seek, and we will issue, a writ of mandamus to ensure compliance with our decisions.

Vacated and Remanded.