  Recently, Barber and Cand\`es 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 $\alpha$, the FDP in the list of discoveries can significantly
exceed $\alpha$. We offer FDP-SD, a new procedure that rigorously controls the
FDP in the competition (knockoff / TDC) setup by guaranteeing that the FDP is
bounded by $\alpha$ at any desired confidence level. Compared with the
just-published general framework of Katsevich and Ramdas, FDP-SD generally
delivers more power and often substantially so in simulated as well as real
data.
