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A large body of research exists around the idea of channel shortening, where a prefilter is designed to reduce the effective channel impulse response to some smaller number of contiguous taps. This idea was originally conceived to reduce the complexity of Viterbi-based maximum-likelihood equalizers. Here, we consider a generalization of channel shortening which we term "channel sparsening". In this case, a prefilter is designed to reduce the effective channel to a small number of nonzero taps which do not need to be contiguous. When used in combination with belief-propagation-based maximum a posteriori (MAP) detectors, an analogous complexity reduction can be realized. We address the design aspects of sparsening filters, including several approaches to minimize the bit error rate of MAP detectors. We devote attention to the interaction of the sparsening filter and detector, and demonstrate the performance gains through simulation.