The FM-index is a data structure which is seeing more and more pervasive use, in particular in the field of high-throughput bioinformatics. Algorithms based on it show a pseudo-random memory access pattern. As a consequence, they are usually bound by memory bandwidth rather than CPU usage. Naive GPU implementations are no exception. Here we show that the combination of a compact design of the FM-index and a thread-cooperative approach can be used to restore a proper balance. The resulting solution is less memory-bandwidth intensive, and allows full exploitation of the computational resources of the GPU across several GPU architectures.