Consider a binary-input, M-output discrete memoryless channel (DMC) where the outputs are quantized to K levels, with K < M. The subject of this paper is the maximization of mutual information between the input and quantizer output, over both the input distribution and channel quantizer. This can be regarded as finding the capacity of a quantized DMC. An algorithm is given, which either finds the optimal input distribution and corresponding quantizer, or declares a failure.