In most species of social insects, the nest is enlarged gradually as the colony grows. Here we call attention to some striking exceptions to this general rule of continuous nest construction. A common pattern among the swarm-founding, eusocial wasp species is explosive nest construction, in which the nest is built rapidly to a large size in the first one to three weeks after colony initiation. Nest size then remains static for weeks or months. We document this pattern of nest growth for the swarm-founding wasp, Polybia occidentalis. Data showing a high percentage of empty cells in pre-emergence-stage nests suggest that a similar pattern holds for some other swarm-founding polistine genera. In contrast, certain other genera seem to follow the continuous construction pattern of the independent founders. We propose five potential factors that could favor a strategy of explosive nest construction: maximization of colony productivity, work-group efficiency, protection of the brood, protection of the swarm adults, and enhancement of reproductive competition. We discuss evidence from both groups of swarm founders that provides circumstantial support for some of these, but not for others.