This paper is about Translation Dictation with ASR, that is, the use of Automatic Speech Recognition (ASR) by human translators, in order to dictate translations. We are particularly interested in the productivity gains that this could provide over conventional keyboard input, and ways in which such gains might be increased through a combination of ASR and Statistical Machine Translation (SMT). In this hybrid technology, the source language text is presented to both the human translator and a SMT system. The latter produces N-best translations hypotheses, which are then used to fine tune the ASR language model and vocabulary towards utterances which are probable translations of source text sentences. We conducted an ergonomic experiment with eight professional translators dictating into French, using a top of the line off-the-shelf ASR system (Dragon NatuallySpeaking 8). We found that the ASR system had an average Word Error Rate (WER) of 11.7 percent, and that translation using this system did not provide statistically significant productivity increases over keyboard input, when following the manufacturer recommended procedure for error correction. However, we found indications that, even in its current imperfect state, French ASR might be beneficial to translators who are already used to dictation (either with ASR or a dictaphone), but more focused experiments are needed to confirm this. We also found that dictation using an ASR with WER of 4 percent or less would have resulted in statistically significant (p less than 0.6) productivity gains in the order of 25.1 percent to 44.9 percent Translated Words Per Minute. We also evaluated the extent to which the limited manufacturer provided Domain Adaptation features could be used to positively bias the ASR using SMT hypotheses. We found that the relative gains in WER were much lower than has been reported in the literature for tighter integration of SMT with ASR, pointing the advantages of tight integration approaches and the need for more research in that area.