Traditional allocators for network-on-chip (NoC) routers suffer from either poor-matching quality or limited fairness. We propose a waterfall (WTF) allocator targeting homogeneous resource allocation, which provides single-cycle maximal matching while guaranteeing strong fairness based on the round-robin principle. It can be implemented with a loop-free structure. In 90 nm technology, the allocator operates at about 1 GHz clock frequency. We compare WTF with wave-front, separable-input-first, and separable-output-first allocators and find that it is at least 10% smaller, has 50% less delay under high load, and uses 3% less power than any of these alternatives. Also, WTF is at least as fair or clearly fairer. We also find that in a 4 $\,\times\,$ 4 circuit switched NoC the use of WTF gives up to 20% higher network performance.