High-performance interconnects need congestion control to deal with traffic bursts. In this paper, we propose ACCurate, a congestion control protocol that assigns exact maxmin fair rates to flows, without relying on costly per-flow state inside the network. ACCurate keeps the backlogs outside of the network, protects innocent flows, and promptly recovers the flows’ rates after congestive episodes. Comparisons with TCP and PAUSE-only RDMA under datacenter-resembling workloads further show that ACCurate provides up to 10x faster flow completion times. ACCurate relies on simple hardware that can be readily implemented inside switches. In our implementation, the additional circuitry needed in a 16x16 switch occupies less than 2% of FPGA resources.