We build a satisficing model of choice under risk which embeds Expected Utility Theory (EUT) into a boundedly rational deliberation process. The decision maker accumulates evidence for and against alternative options by repeatedly sampling from her underlying set of EU preferences until the evidence favouring one option satisfies her desired level of confidence. Despite its EUT core, the model produces patterns of behaviour that violate standard EUT axioms, while at the same time capturing systematic relationships between choice probabilities, response times and confidence judgments, which are beyond the scope of theories that do not take deliberation into account.