Historical accounts of human achievement suggest that accidents can play an important role in innovation. In this paper, we seek to contribute to an understanding of how digital systems might support valuable unpredictability in innovation processes by examining how innovators who obtain value from accidents integrate unpredictability into their work. We describe an inductive, grounded theory project, based on 20 case studies, that looks into the conditions under which people who make things keep their work open to accident, the degree to which they rely on accidents in their work, and how they incorporate accidents into their deliberate processes and arranged surroundings. By comparing makers working in varied conditions, we identify specific factors (e.g., technologies, characteristics of technologies) that appear to support accidental innovation. We show that makers in certain specified conditions not only remain open to accident but also intentionally design their processes and surroundings to invite and exploit valuable accidents. Based on these findings, we offer advice for the design of digital systems to support innovation processes that can access valuable unpredictability.