The paper presents an overview of the Spoken Language Translator (SLT) system's hybrid language-processing architecture, focussing on the way in which rule-based and statistical methods are combined to achieve robust and efficient performance within a linguistically motivated framework. In general, we argue that rules are desirable in order to encode domain-independent linguistic constraints and achieve high-quality grammatical output, while corpus-derived statistics are needed if systems are to be efficient and robust; further, that hybrid architectures are superior from the point of view of portability to architectures which only make use of one type of information. We address the topics of ``multi-engine'' strategies for robust translation; robust bottom-up parsing using pruning and grammar specialization; rational development of linguistic rule-sets using balanced domain corpora; and efficient supervised training by interactive disambiguation. All work described is fully implemented in the current version of the SLT-2 system.