Critical incident exercises (CIEs) are increasingly used in English courses, and there seems little doubt that in addition to providing English practice opportunities CIEs also help learners build intercultural competence. The question is: What precise aspects of intercultural competence do CIEs help learners build? This article introduces an open-ended variety of CIE called an "encounter exercise," and explores the aspects of intercultural competence regular use of such exercises helps learners build. Drawing on recent literature about dual-process views of thinking, this article argues that encounter exercises are valuable for helping learners build the following habits of thought: (1) being consciously aware of the interpretation process in intercultural communication situations, (2) consciously considering multiple interpretations of puzzling or problematic intercultural encounters, (3) paying conscious attention to factors that may affect how one interprets problematic intercultural encounters, especially factors that affect feelings or interpretation rules, and (4) paying conscious attention to the "benefit-of-the-doubt" question.