A microprocessor includes a hierarchical memory subsystem, an instruction decoder, and a stream prefetch unit. The decoder decodes an instruction that specifies a locality characteristic parameter. In one embodiment, the parameter specifies a relative urgency with which a data stream specified by the instruction is needed rather than specifying exactly which of the cache memories in the hierarchy to prefetch the data stream into. The prefetch unit selects one of the cache memory levels in the hierarchy for prefetching the data stream into based on the memory subsystem configuration and on the relative urgency. In another embodiment, the prefetch unit instructs the memory subsystem to mark the prefetched cache line for early, late, or normal eviction according to its cache line replacement policy based on the parameter value.