Most space-time coding schemes can be classified either as non-coherent (decoding is performed without forming an explicit channel estimate) or coherent (decoding is performed conditioned upon a channel estimate as if it were the actual channel realisation). In this paper we prove that optimal non-coherent decoding can be decomposed into a channel estimation step, followed by coherent decoding step. Surprisingly the required estimators do not in general minimise the mean squared error between the estimated and actual channel. We also investigate the role of training sequences in such systems.