Shannon’s Noisy-Channel model, which describes how a corrupted message might be reconstructed, has been the corner stone for much work in statistical language and speech processing. The model factors into two components: a language model to characterize the original message and a channel model to describe the channel’s corruptive process. The standard approach for estimating the parameters of the channel model is unsupervised Maximum-Likelihood of the observation data, usually approximated using the Expectation-Maximization (EM) algorithm. In this paper we show that it is better to maximize the joint likelihood of the data at both ends of the noisy-channel. We derive a corresponding bi-directional EM algorithm and show that it gives better performance than standard EM on two tasks: (1) translation using a probabilistic lexicon and (2) adaptation of a part-of-speech tagger between related languages.