In this paper, we consider how the structures of tasks and teams interact to affect team performance. We study the effects of diversity in experience on a team's ability to respond to task changes by separately examining interpersonal team diversity (i.e., differences in experience across the entire team) and intrapersonal team diversity (i.e., whether individuals on the team are more or less specialized). We also examine whether team familiarity—team members' prior experience working with one another—helps teams to better manage challenges created by task changes and greater interpersonal team diversity. Using detailed project- and individual-level data from an Indian software services firm, we find that the interaction of task change with intrapersonal diversity is related to improved project performance, whereas the interaction of task change with interpersonal diversity is related to diminished performance. Additionally, the interaction of team familiarity with interpersonal diversity is related to improved project performance in some cases. Our results highlight a need for more nuanced approaches to leveraging experience in team management.