Often, the sound arriving at the ears is a mixture from many different sources, but only 1 is of interest. To assist with selection, the auditory system structures the incoming input into streams, each of which ideally corresponds to a single source. Some authors have argued that this process of streaming is automatic and invariant, but recent evidence suggests it is affected by attention. In Experiments 1 and 2, it is shown that the effect of attention is not a general suppression of streaming on an unattended side of the ascending auditory pathway or in unattended frequency regions. Experiments 3 and 4 investigate the effect on streaming of physical gaps in the sequence and of brief switches in attention away from a sequence. The results demonstrate that after even short gaps or brief switches in attention, streaming is reset. The implications are discussed, and a hierarchical decomposition model is proposed.