The problem of detecting a sinusoid with drifting phase in the presence of additive white Gaussian noise is considered. A Lorentzian signal model is used, in which the signal to be detected is modeled as a sinusoid whose phase is drifting with Brownian motion. A class of quadratic detectors that trade off coherent and noncoherent averaging of the received waveform is studied. The deflection ratio is used as a performance criterion, and the optimum quadratic detector structure as parametrized by the phase bandwidth is derived. Then, the performance relative to the optimum of a class of suboptical detectors calledm‐order noncoherent detectorsis considered. It is shown that the best detector in this class performs nearly as well as the optimum quadratic detector. This is in sharp contrast with standard envelope detection whose performance is shown to degrade severely in the presence of phase drift. Simulated detection probabilities that verify this performance disparity are also presented.