It is difficult to directly apply traditional speaker identification (SID) systems to cochannel speech, mixtures from two speakers. Previous work demonstrates that extraction of usable speech segments significantly improves SID performance if speaker assignment, or sequential organization of the segments, is known. We derive a joint computational objective for speaker assignment and cochannel SID, leading to a problem of search for the optimum hypothesis. We propose a hypothesis pruning method based on speaker models to make the search computationally feasible. Evaluation results show that the proposed algorithm approaches the ceiling SID performance obtained with prior pitch information, and yields significant improvement over alternative approaches on speaker assignment.