Cochannel interference affects not only the signal quality, but also the capacity of most wireless cellular networks. Unlike in spread spectrum communications, in systems employing non-spread signals, cochannel signal suppression is expensive. Moreover, at the portable station, joint estimation rather than suppression of the cochannel signal(s) may be a cheaper alternative and may oftentimes also provide a better signal quality. In this work we propose a novel two-stage joint Viterbi algorithm with full feedback. This technique, which is sub-optimal to the ideal joint maximum likelihood sequence estimator, provides an excellent way to trade complexity for performance, and is amenable for single-input mobile and hand-held receiver implementations.