Sounds consisting of multiple simultaneous or consecutive components can be detected by listeners when the stimulus levels of the components are lower than those needed to detect the individual components alone. The mechanisms underlying such spectral, spectrotemporal, temporal, or across-ear integration are not completely understood. Here, we report threshold measurements from human subjects for multicomponent stimuli (tone complexes, tone sequences, diotic or dichotic tones) and for their individual sinusoidal components in quiet. We examine whether the data are compatible with the detection model developed by Heil, Matysiak, and Neubauer (HMN model) to account for temporal integration (Heil et al. 2017), and we compare its performance to that of the statistical summation model (Green 1958), the model commonly used to account for spectral and spectrotemporal integration. In addition, we compare the performance of both models with respect to previously published thresholds for sequences of identical tones and for diotic tones. The HMN model is similar to the statistical summation model but is based on the assumption that the decision variable is a number of sensory events generated by the components via independent Poisson point processes. The rate of events is low without stimulation and increases with stimulation. The increase is proportional to the time-varying amplitude envelope of the bandpass-filtered component(s) raised to an exponent of 3. For an ideal observer, the decision variable is the sum of the events from all channels carrying information, for as long as they carry information. We find that the HMN model provides a better account of the thresholds for multicomponent stimuli than the statistical summation model, and it offers a unifying account of spectral, spectrotemporal, temporal, and across-ear integration at threshold.