This paper explores how accountability might make otherwise obscure and inaccessible algorithms available for governance. The potential import and difficulty of accountability is made clear in the compelling narrative reproduced across recent popular and academic reports. Through this narrative we are told that algorithms trap us and control our lives, undermine our privacy, have power and an independent agential impact, at the same time as being inaccessible, reducing our opportunities for critical engagement. The paper suggests that STS sensibilities can provide (...) a basis for scrutinizing the terms of the compelling narrative, disturbing the notion that algorithms have a single, essential characteristic and a predictable power or agency. In place of taking for granted the terms of the compelling narrative, ethnomethodological work on sense-making accounts is drawn together with more conventional approaches to accountability focused on openness and transparency. The paper uses empirical material from a study of the development of an “ethical,” “smart” algorithmic videosurveillance system. The paper introduces the “ethical” algorithmic surveillance system, the approach to accountability developed, and some of the challenges of attempting algorithmic accountability in action. The paper concludes with reflections on future questions of algorithms and accountability. (shrink)