This book argues that while some adjuncts and complements contribute regular assertions, others operate in the conventional implicature dimension, which expresses additional side comments. This distinction of semantic dimension is shown as necessary to account for regular vs. speech act uses of ‘weil’ vs. ‘denn’ (because) in German, for regular vs. relevance conditionals, as well as certain sentence adverbs. Further, a new two-dimensional analysis is crucial to account for the differences between parenthetical-like sliftings and true verb-second embedded clauses in German.