In many listening situations, information about the spectral content of a target sound may be distributed over time, and estimating the target spectrum requires efficient sequential processing. Listeners' ability to estimate the spectrum of a random-frequency, six-tone complex was investigated and the spectral content of the complex was revealed using a sequence of bursts. Whether each of the six tones was presented within each burst was determined at random according to a presentation probability. In separate conditions, the presentation probabilities (p) ranged from 0.2 to 1, the total number of bursts varied from 1 to 16, and the inter-burst interval was either 0 or 200 ms. To evaluate the information acquired by the listener, the burst sequence was followed, after a 500-ms silent interval, by the six-tone complex acting as an informational masker and the listener was required to detect a pure-tone target presented simultaneously with the masker. Greater performance in this task indicates more accurate estimation of the spectrum of the complex by the listener. Evidence for integration of information across bursts was observed, and the integration process did not significantly depend on inter-burst interval.