Coherence misses in shared-memory multiprocessors account for a substantial fraction of execution time in many important scientific and commercial workloads. Memory streaming provides a promising solution to the coherence miss bottleneck because it improves memory level parallelism and lookahead while using on-chip resources efficiently. We observe that the order in which shared data are consumed by one processor is correlated to the order in which they were produced by another. We investigate this phenomenon and demonstrate that it can be exploited to send Store-ORDered Streams (SORDS) of shared data from producers to consumers, thereby eliminating coherent read misses. Using a trace-driven analysis of all user and OS memory references in a cache-coherent distributed shared-memory multiprocessor, we show that SORDS-based memory streaming can eliminate between 36% and 100% of all coherent read misses in scientific workloads and between 23% and 48% in online transaction processing workloads.