The purpose of this study was to characterize variations in how teachers enacted an approach to ambitious mathematics teaching: "rough draft math." We also examined teachers' motivations for their enactments. Thirty-two teachers from five states in the U.S.A. were recruited to participate in interviews based on recommendations from leaders of book studies focusing on this teaching practice. All participants enacted "rough draft math" by intentionally building their classroom culture to welcome students' draft thinking to achieve the goal of promoting students' productive dispositions. However, additional variations in enactments drew attention to potential tensions between multiple goals of ambitious mathematics teaching (empowering students and learning through revising). Findings suggest insights for supporting teachers' learning to teach ambitiously; findings also contribute to a knowledge base for teaching. [For the complete proceedings, see ED630210.]