Causal queries about singular cases are ubiquitous, yet the question how we assess whether a particular outcome was actually caused by a specific potential cause turns out to be difficult to answer. Relying on the causal power approach, Cheng and Novick (2005) proposed a model of causal attribution intended to help answering this question. We challenge this model, both conceptually and empirically. The central problem of this model is that it treats the presence of sufficient causes as necessarily causal in singular causation, and thus neglects that causes can be preempted in their efficacy. Also, the model neglects that reasoners incorporate uncertainty about the underlying causal structure and strengths of causes when making causal inferences. We propose a new measure of causal attribution and embed it into our structure induction model of singular causation (SISC). Two experiments support the model.