In decision making, speed-accuracy trade-offs are well known and often inevitable because accuracy depends on being well informed and gathering information takes time. However, trade-offs between speed and cohesion, that is the degree to which a group remains together as a single entity, as a result of their decision making, have been comparatively neglected. We combine theory and experimentation to show that in decision-making systems, speed-cohesion trade-offs are a natural complement to speed-accuracy trade-offs and are therefore of general importance. We then analyse the decision performance of 32 rock ant, Temnothorax albipennis, colonies in experiments in which accuracy of collective decision making was held constant, but time urgency varied. These experiments reveal for the first time an adaptive speed-cohesion trade-off in collective decision making and how this is achieved. In accord with different time constraints, colonies can decide quickly, at the cost of social unity, or they can decide slowly with much greater cohesion. We discuss the similarity between cohesion and the term precision as used in statistics and engineering. This emphasizes the generality of speed versus cohesion/precision trade-offs in decision making and decision implementation in other fields within animal behaviour such as sexually selected motor displays and even certain aspects of birdsong. We also suggest that speed versus precision trade-offs may occur when individuals within a group need to synchronize their activity, and in collective navigation, cooperative hunting and in certain escape behaviours.