The leader election problem is a fundamental distributed coordination problem. We present leader election algorithms for the cache-coherent (CC) and distributed shared memory (DSM) models using reads and writes only, for which the number of remote memory references (RMRs) is constant in the worst case. The algorithms use splitter-like objects [6, 8] in a novel way for the efficient partitioning of processes into disjoint sets that share work. As there is an Ω(log n/ log log n) lower bound on the RMR complexity of mutual exclusion for n processes using reads and writes only , our result separates the mutual exclusion and leader election problems in terms of RMR complexity in both the CC and DSM models. Our result also implies that any algorithm using reads, writes and one-time test-and-set objects can be simulated by an algorithm using reads and writes with only a constant blowup of the RMR complexity. Anderson, Herman and Kim raise the question of whether conditional primitives such as test-and-set and compare-and-swap are stronger than read and write for the implementation of local-spin mutual exclusion . We provide a negative answer to this question, at least for one-time test-and-set.