: Three fast mutual exclusion algorithms using read-modify-write and atomic read/write registers are presented in a sequence, with an improvement from one to the next. The last algorithm is shown to be optimal in minimizing the number of remote memory accesses required in a resource busy period. Remote memory access is the key factor of memory access bottleneck in large shared-memory multiprocessors. The algorithm is particularly suitable in such systems for applications with small critical sections and frequent resource requests.