The disclosed embodiments relate to a system that generates prefetches for a stream of data accesses with multiple strides. During operation, while a processor is generating the stream of data accesses, the system examines a sequence of strides associated with the stream of data accesses. Next, upon detecting a pattern having a single constant stride in the examined sequence of strides, the system issues prefetch instructions to prefetch a sequence of data cache lines consistent with the single constant stride. Similarly, upon detecting a recurring pattern having two or more different strides in the examined sequence of strides, the system issues prefetch instructions to prefetch a sequence of data cache lines consistent with the recurring pattern having two or more different strides.