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Recently, Barber and Candès laid the theoretical foundation for a general framework for false discovery rate (FDR) control based on the notion of "knockoffs." A closely related FDR control methodology has long been employed in the analysis of mass spectrometry data, referred to there as "target–decoy competition" (TDC). However, any approach that aims to control the FDR, which is defined as the expected value of the false discovery proportion (FDP), suffers from a problem. Specifically, even when successfully controlling the FDR at level α, the FDP in the list of discoveries can significantly exceed α. We offer FDP‐SD, a new procedure that rigorously controls the FDP in the knockoff/TDC competition setup by guaranteeing that the FDP is bounded by α at a desired confidence level. Compared with the recently published framework of Katsevich and Ramdas, FDP‐SD generally delivers more power and often substantially so in simulated and real data. [ABSTRACT FROM AUTHOR]