Arrangements and method for enabling and disabling cache bypass in a computer system with a cache hierarchy. Cache bypass status is identified with respect to at least one cache line. A cache line identified as cache bypass enabled is transferred to one or more higher level caches of the cache hierarchy, whereby a next higher level cache in the cache hierarchy is bypassed, while a cache line identified as cache bypass disabled is transferred to one or more higher level caches of the cache hierarchy, whereby a next higher level cache in the cache hierarchy is not bypassed. Included is an arrangement for selectively enabling or disabling cache bypass with respect to at least one cache line based on historical cache access information.