We describe a series of experiments in which we start with English to French and English to Japanese versions of a rule-based speech translation system for a medical domain, and bootstrap corresponding statistical systems. Comparative evaluation reveals that the statistical systems are still slightly inferior to the rule-based ones, despite the fact that con- siderable effort has been invested in tuning both the recognition and translation components; however, a hybrid system is able to deliver a small but significant improvement in performance. In conclusion, we suggest that the hybrid architecture we describe potentially allows construction of limited-domain speech translation systems which combine substantial source-language coverage with high-precision translation.