In this paper we describe moral quasi-dilemmas (MQDs): situations similar to moral dilemmas, but in which an agent is unsure whether exploring the plan space or the world may reveal a course of action that satisfies all moral requirements. We argue that artificial moral agents (AMAs) should be built to handle MQDs (in particular, by exploring the plan space rather than immediately accepting the inevitability of the moral dilemma), and that MQDs may be useful for evaluating AMA architectures.