Summary: We propose the new Group Metric (GM) soft-decision decoder for convolutionally coded synchronous multiple-access channels. The GM decoder exploits the independently operating encoders of the multiuser channel by making decoding decisions for a subset of the users, but incorporating all the multiuser information in its metrics. For a single user, this decoder will have a reduced complexity that is exponential in the sum of encoder memory and the number of users. The soft-decision Maximum-Likelihood (ML) joint decoder is well known. This optimal decoder suffers from a high complexity requirement that is exponential in the product of encoder memory and the number of users. The size of the decoded subset is a design parameter which allows a tradeoff between complexity and performance. The performance of the GM decoder, once properly characterized, can be analyzed using standard techniques. In addition, a new analysis technique is presented which considers decomposable sequences for the fading channel. With this analysis, we have a new tool for bounding error probabilities for multiuser decoders. Applying this technique to the GM decoder, we can directly identify sequences that are decomposable some fraction of the time and obtain a new upper bound. Further, this improved bound can be expressed in closed form. Numerical results show that the actual performance gap between the GM and ML decoders can be quite small.