The state of the art congestion control algorithms for wireless sensor networks respond to coarse-grained feedback regarding available capacity in the network with an additive increase multiplicative decrease mechanism to set source rates. Providing precise feedback is challenging in wireless networks because link capacities vary with traffic on interfering links. We address this challenge by applying a receiver capacity model that associates capacities with nodes instead of links, and use it to develop and implement the first explicit and precise distributed rate-based congestion control protocol for wireless sensor networks — the wireless rate control protocol (WRCP). Apart from congestion control, WRCP has been designed to achieve lexicographic max-min fairness. Through extensive experimental evaluation on the USC Tutornet wireless sensor network testbed, we show that WRCP offers substantial improvements over the state of the art in flow completion times as well as in end-to-e...