Searches for signals of new physics in particle physics are usually done by training a supervised classifier to separate a signal model from the known Standard Model physics (also called the background model). However, even when the signal model is correct, systematic errors in the background model can influence supervised classifiers and might adversely affect the signal detection procedure. To tackle this problem, one approach is to use the (possibly misspecified) classifier only to perform a preliminary signal-enrichment step and then to carry out a signal detection test on the signal-rich sample. For this procedure to work, we need a classifier constrained to be decorrelated with one or more protected variables used for the signal-detection step. We do this by considering an optimal transport map of the classifier output that makes it independent of the protected variable(s) for the background. We then fit a semiparametric mixture model to the distribution of the protected variable after making cuts on the transformed classifier to detect the presence of a signal. We compare and contrast this decorrelation method with previous approaches, show that the decorrelation procedure is robust to moderate background misspecification, and analyze the power and validity of the signal detection test as a function of the cut on the classifier both with and without decorrelation. We conclude that decorrelation and signal enrichment help produce a stable, robust, valid, and more powerful test.