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The problem of distributed sequential detection in the presence of communication constraints is considered. The observations available at each sensor are first compressed to multibit sensor decisions and sent to the fusion center. At the fusion center, a sequential data fusion scheme is implemented in order to reach a global decision. An algorithm is developed for optimal bandwidth distribution among sensors under a fixed bandwidth constraint. Under symmetry and conditional independence assumptions, the algorithm can be simplified substantially: the cooperative quantizer design algorithm reduces to independent quantizer design. The case when communication bandwidth is the only constraint is also considered.