Efficient cooperation often requires coordination, such that exactly one of two players takes an available action. If the decisions whether to pursue the action are made simultaneously, then neither or both may acquiesce leading to an inefficient outcome. However, inefficiency may be reduced if players move sequentially. We test this experimentally by introducing repeated two-stage versions of such a game where the action is individually profitable. In one version, players may wait in the first stage to see what their partner did and then coordinate in the second stage. In another version, sequential decision-making is imposed by assigning one player to move in stage one and the other in stage two. Although there are fewer cooperative decisions in the two-stage treatments, we show that overall subjects coordinate better on efficient cooperation and on avoiding both acquiescing. Yet, only some pairs actually achieve higher profits, while the least cooperative pairs do worse in the two-stage games than their single-stage counterparts. For these, rather than facilitating coordination, the additional stage invites attempts to disguise uncooperative play, which are met with punishment.