In the auditory detection of a sinusoidal signal in the presence of random noise, it has previously been demonstrated that the presence of a “pedestal” or background sinusoid of the same frequency and phase as the signal increases detectability. This increase was confirmed in a two‐interval forced choice experiment in which a 1000‐cps sinusoid was present in one of two 0.1‐sec intervals, and the noise plus pedestal were present in both intervals. Pedestals of moderate intensity in phase with the signal increased detectability. Pedestals in quadrature (90° out of phase) with the signal did not improve detectability. Very large pedestals decreased detectability irrespective of phase. A simple energy‐detection model was developed and its performance compared with the experimental results. The model consists of a bandpass filter, a square‐law element, and an integrator. The probability of correct detection varies with signal level in a manner similar to the auditory results. Detectability is improved by an in‐phase pedestal and approaches that of a correlation detector in the limit of infinite pedestal. Detectability is not improved by quadrate pedestals. The model can be modified to predict the decreasing detectability with large pedestals.