There are two main strands in conference interpretation teaching - one placing greater emphasis on building up language conversion skills, the other on spontaneous rendition of sense. In teaching simultaneous interpretation into B, there is a risk of the two becoming intertwined to a confusing extent. Weak intuition in B language expression, grammatical and pronunciation difficulties, the influence of the A language all tend to focus the attention of both students and instructors on language-related issues. Yet the sense transmission paradigm that underpins teaching in many institutions would seem to be of particular relevance to learning to interpret in a sensitive and structured way into B. The latter point is considered and taken as a premise for the definition of teaching methods that will circumvent the language-switch versus sense dilemma. In particular, the appropriate place of language enhancement, the importance of background knowledge and of preparation, and course design are examined.