Swarms consist of many agents that interact according to a simple set of rules, giving rise to emergent global behaviours. In this paper, we consider swarms of mobile robots or drones. Swarms can be tolerant of faults that may occur for many reasons, such as resource exhaustion, component failure, or disruption from an external event. The loss of agents reduces the size of a swarm, and may create an irregular structure in the swarm topology. A swarm’s structure can also be irregular due to initial conditions, or the existence of an obstacle. These changes in the structure or size of a swarm do not stop it from functioning, but may adversely affect its efficiency or effectiveness. In this paper, we describe a self-healing mechanism to counter the effect of agent loss or structural irregularity. This method is based on the reduction of concave regions at swarm perimeter regions. Importantly, this method requires no expensive communication infrastructure, relying only on agent proximity information. We illustrate the application of our method to the problem of surrounding an oil slick, and show that void reduction is necessary for full and close containment, before concluding with a brief discussion of its potential uses in other domains.