1. A method of fetching instructions and/or operands along a path which may not be taken by a process being executed by a computer processor having a hierarchical memory structure with data being loaded into cache lines of a cache in the structure comprising the steps of, making selected hedge fetches sensitive to whether the data is in the cache so as to gain the best performance advantage with a selected hedge fetch signal which accompanies each fetch request to the cache to identify whether a line should be loaded if it misses the cache to indicate a selected hedge fetch when this signal is ON, and rejecting a fetch request in the event the selected hedge fetch signal is turned ON if the data is not in the cache, the cache will reject the fetch, and thereafter repeating the fetch request after a fetch request has been rejected when the the selected hedge fetch signal was turned ON the data was not in the cache to repeat the fetch request at a later time when it is more certain that the process being executed wants the data, or never repeating the request upon determination that the process being executed does not need the data to be fetched, and wherein the determination of which fetches are marked by a selected hedge fetch signal which accompanies each fetch request to the cache to identify whether a line should be loaded if it misses the cache to indicate a selected hedge fetch when this signal is ON, is determined by the setting of latches which control which fetches are so treated, and the determination of which latches are set is determined by testing combinations of fetches treated this way to determine which performs best.