A method, processor, and data processing system for dynamically adjusting a prefetch stream priority based on the consumption rate of the data by the processor. The method includes a prefetch engine issuing a prefetch request of a first prefetch stream to fetch one or more data from the memory subsystem. The first prefetch stream has a first assigned priority that determines a relative order for scheduling prefetch requests of the first prefetch stream relative to other prefetch requests of other prefetch streams. Based on the receipt of a processor demand for the data before the data returns to the cache or return of the data along time before the receiving the processor demand, logic of the prefetch engine dynamically changes the first assigned priority to a second higher or lower priority, which priority is subsequently utilized to schedule and issue a next prefetch request of the first prefetch stream.