A variety of joint action studies show that people tend to fall into synchronous behavior with others participating in the same task, and that such synchronization is beneficial, leading to greater rapport, satisfaction, and performance. It has been noted that many of these task environments require simple interactions that involve little planning of action coordination toward a shared goal. The present study utilized a complex joint construction task in which dyads were instructed to build model cars while their hand movements and heart rates were measured. Participants built these models under varying conditions, delimiting how freely they could divide labor during a build session. While hand movement synchrony was sensitive to the different tasks and outcomes, the heart rate measure did not show any effects of interpersonal synchrony. Results for hand movements show that the more participants were constrained by a particular building strategy, the greater their behavioral synchrony. Within the different conditions, the degree of synchrony was predictive of subjective satisfaction and objective product outcomes. However, in contrast to many previous findings, synchrony was negatively associated with superior products, and, depending on the constraints on the interaction, positively or negatively correlated with higher subjective satisfaction. These results show that the task context critically shapes the role of synchronization during joint action, and that in more complex tasks, not synchronization of behavior, but rather complementary types of behavior may be associated with superior task outcomes.