Statistical Machine Translation produces results that make it a competitive option in most machine-assisted translation scenarios. However, these good results often come at a very high computational cost and correspond to training regimes which are unfit to many practical contexts, where the ability to adapt to users and domains and to continuously integrate new data (eg. in post-edition contexts) are of primary importance. In this article, we show how these requirements can be met using a strategy for on-demand word alignment and model estimation. Most remarkably, our incremental system development framework is shown to deliver top quality translation performance even in the absence of tuning, and to surpass a strong baseline when performing online tuning. All these results obtained with great computational savings as compared to conventional systems.