Abstract The vast majority of compact binary mergers in the Universe produce gravitational waves that are too weak to yield unambiguous detections; they are unresolved. We present a method to infer the population properties of compact binaries—such as their merger rates, mass spectrum, and spin distribution—using both resolved and unresolved gravitational waves. By eliminating entirely the distinction between resolved and unresolved signals, we eliminate bias from selection effects. To demonstrate this method, we carry out a Monte Carlo study using an astrophysically motivated population of binary black holes. We show that some population properties of compact binaries are well constrained by unresolved signals after about one week of observation with Advanced LIGO at design sensitivity.