This paper contributes to the understanding of accountability in its relation with responsibility. It applies Derrida’s work on responsibility, testimony, and gift to the problematic of accountability. Accountability’s entanglement in the tension between, morality and ethics, singular and general responsibilities is examined, and Derrida’s analysis of the aporia of responsibility is expressed and explored in terms of an aporia of accountability: It is argued that accountability relies on responsibility but that the rendering of accountability tends to undermine responsibility. In seeking to make a positive contribution to the question of how accountability might contribute to raising levels of responsibility for the other, the wholly other, the paper critically builds on existing Levinasian perspectives on this question, and develops the suggestion, inspired by Derrida’s work, that in appropriate circumstances the reconfiguring of accountability as testimony and as gift might help enhance responsibility.