The perception of multiple pitches evoked by concurrent periodic sounds is modeled as a process by which the sounds are canceled in turn (multistep cancellation model) or simultaneously (joint cancellation model). As an example of multistep cancellation, the pitch perception model of Meddis and Hewitt (1991a,b) is associated with the concurrent vowel identification model of Meddis and Hewitt (1992). A first period estimate is used to suppress correlates of the dominant sound. A second period is then estimated from the remainder. Pitches are derived from both period estimates. The process may be repeated to recursively refine the initial estimates, or else to estimate further pitches. This particular model is spectrotemporal (filter channel selection based on temporal cues) but multistep cancellation can also be performed in the spectral or time domain. In the joint cancellation model, estimation and cancellation are performed together in the time domain: the parameter space of several cascaded cancellation filters is searched exhaustively for a minimum output. The parameters that yield this minimum are the period estimates. Joint cancellation is {\em guaranteed}\ to find all periods, except in certain situations for which the stimulus is inherently ambiguous. Multistep and joint cancellation are closely related and give similar results.