This article describes the increasing pressures on those who teach graduate seminars in composition pedagogy to cover a broad range of texts, topics, and techniques. It argues that in response, pedagogy instructors may need to deliberately (re)design their courses in order to continue to help new writing instructors engage in inquiry and discovery, to help them learn to "think like teachers." Specifically, it recommends two kinds of un-coverage strategies. The first is a problem-based pedagogy, such as one described by Wendy Swyt that features reading-clusters and a "contact-zone" approach, or one that focuses on investigating "unsolvable problems" in composition pedagogy. The second is a discovery-draft pedagogy, one that uses exploratory, challenging writing assignments and writing workshops to engage students in reflection and inquiry.