Previous research has shown that power increases focus on the main goal when distractor information is present. As a result, high-power people have been described as goal-focused. In real life, one typically wants to pursue multiple goals at the same time. There is a lack of research on how power affects how people deal with situations in which multiple important goals are present. To address this question, 158 participants were primed with high or low power or assigned to a control condition, and were asked to perform a dual-goal task with three difficulty levels. We hypothesized and found that high-power primed people prioritize when confronted with a multiple-goal situation. More specifically, when task demands were relatively low, power had no effect; participants generally pursued multiple goals in parallel. However, when task demands were high, the participants in the high-power condition focused on a single goal whereas participants in the low-power condition continued using a dualtask strategy. This study extends existing power theories and research in the domain of goal pursuit.