Using machine translation output as a starting point for human translation has become an increasingly common application of MT. We propose and evaluate three computationally efficient online methods for updating statistical MT systems in a scenario where post-edited MT output is constantly being returned to the system: (1) adding new rules to the translation model from the post-edited content, (2) updating a Bayesian language model of the target language that is used by the MT system, and (3) updating the MT system's discriminative parameters with a MIRA step. Individually, these techniques can substantially improve MT quality, even over strong baselines. Moreover, we see super-additive improvements when all three techniques are used in tandem.