Hundreds of thousands of non-citizens are removed from the United States every year. A frustrating incompatibility — a catch — lies at the heart of the legal standard that determines whether legal permanent residents (LPRs) who are removable from the United States may qualify for cancellation of removal and thereby remain in the country. There is currently a circuit split over how to interpret this incompatibility. In order to qualify to apply for cancellation of removal, LPRs bear the burden of proving by a preponderance of the evidence that they have not been convicted of an aggravated felony. Whether an LPR has been convicted of an aggravated felony is a legal question, resolved by applying a categorical approach comparing the state statute of conviction with the generic federal definition, or a modified categorical approach that permits examination of a limited number of state court documents. The preponderance of the evidence standard, however, is a factual inquiry with a spectrum of possible levels of proof. Requiring LPRs to prove a matter of law by a preponderance of the evidence actually requires, in essence, proof beyond a reasonable doubt.This article argues that an inconclusive record, which shows that an LPR was convicted of some crime but does not establish that the crime was the equivalent of a federal “aggravated felony,” must carry the alien’s burden of proving by a preponderance of the evidence that she was not convicted of an aggravated felony. This is the only means of harmonizing this internally incompatible and contradictory standard.