What motivates a fluent bilingual speaker to switch languages within a single utterance? We propose a novel discourse-functional motivation: less predictable, high information-content meanings are encoded in one language, and more predictable, lower information-content meanings are encoded in another language. Switches to a speaker’s less frequently used, and hence more salient, language offer a distinct encoding that highlights information-rich material that comprehenders should attend to especially carefully. Using a corpus of natural Czech-English bilingual discourse, we test this hypothesis against an extensive set of control factors from sociolinguistic, psycholinguistic, and discourse-functional lines of research using mixed-effects logistic regression, in the first such quantitative multifactorial investigation of codeswitching in discourse. We find, using a Shannon guessing game to quantify predictability of meanings in conversation, that words with difficult-to-guess meanings are indeed more likely to be codeswitch sites, and that this is in fact one of the most highly explanatory factors in predicting the occurrence of codeswitching in our data. We argue that choice of language thus serves as a formal marker of information content in discourse, along with familiar means such as prosody and syntax. We further argue for the utility of rigorous, multifactorial approaches to sociolinguistic speaker choice phenomena in natural conversation.