In the present study, a sample-discrimination procedure is used to examine how various statistical constraints on random, time-varying spectra might aid listeners in discriminating among these signals. Time-varying spectra were constructed by adding five sequences of tones, five tones in each sequence, centered at the octave frequencies from 250 to 4000 Hz. The levels, frequencies, and durations of the tones varied randomly from one presentation to the next. The signal to be detected was an increment in the level of tones comprising the sequence centered at 1000 Hz (the target sequence). Three main conditions were examined in which the parameter values of tones varied independently of one another (equal-variance condition), covaried across tone sequences (cross-channel covariance condition), or covaried among themselves for each tone (cross-parameter covariance condition). For the latter two conditions, two special cases were examined in which the target sequence varied independently of nontarget sequences or varied according to the same statistical rules. For five of six listeners, comparisons of performance to that of an ideal, within-channel observer gave clear evidence of an ability to take advantage of cross-channel statistical constraints, but only when the target sequence varied independently of its context. Results offer no evidence for listeners' ability to take advantage of cross-parameter constraints. Trial-by-trial analyses in the equal-variance condition identify factors other than the appropriate weighting of information as primarily responsible for suboptimal performance, though individual differences complicate this interpretation. A failure of simple detection-theoretic models to account for these results is discussed in terms of possible perceptual rules governing sound source identification of real-world objects.