Memorable teaching–teaching that makes memorable not only the teacher but also what the student has learned–is necessarily strong in both the cognitive and the affective domain. University statistics courses make heavy cognitive demands of students: these demands become more intense as the level of study increases. In such a setting, many students value an opportunity to break away for a while from the focus on technical aspects, to engage with a thematically-related challenge that the teacher has designed to provoke them or to pique their curiosity. We explore the design of such statistical diversions to enrich undergraduate courses at various levels. Diversions seem to be little recognized or utilized in statistics education, yet they can reinvigorate students’ interest in their study of the subject. Diversions can also produce clarifying perspectives and other enlightening insight –characteristic cognitive strengths of memorable teaching.