Sensor networks have traditionally consisted of nodes with the same amounts of resources such a batter life and computational power. While such homogeneity has distinct advantages in terms of ease-of-fabrication, it has also been shown that in multi-hop ad-hoc scenarios homogeneity leads to large duty cycles, small end-to-end data throughput and poor deployment lifetimes. In this paper, we investigate sensor networks that have a single degree of heterogeneity, a random subset of the sensors, called accumulators, have more power and computational capability.