Many approaches for multiple testing begin with the assumption that all tests in a given study should be combined into a global false-discovery-rate analysis. But this may be inappropriate for many of today’s large-scale screening problems, where auxiliary information about each test is often available, and where a combined analysis can lead to poorly calibrated error rates within different subsets of the experiment. To address this issue, we introduce an approach for false-discovery-rate regression (FDRR) that uses this auxiliary information to improve power while maintaining control over the global error rate. The method can be motivated by a hierarchical Bayesian model in which covariates are allowed to influence the local false discovery rate (or equivalently, the posterior probability that a given observation is a signal) via a logistic regression. We apply the method to a data set involving neural recordings from the primary visual cortext. The goal is to detect pairs of neurons that exhibit fine-time-scale interactions, in the sense that they fire together more often than expected due to chance. Our proposed method detects three times as many synchronous pairs as a standard FDR-controlling analysis.