A processor includes a conditional branch instruction prediction mechanism that generates weighted branch prediction values. For weakly weighted predictions, which tend to be less accurate than strongly weighted predictions, the power associating with speculatively filling and subsequently flushing the cache is saved by halting instruction prefetching. Instruction fetching continues when the branch condition is evaluated in the pipeline and the actual next address is known. Alternatively, prefetching may continue out of a cache. To avoid displacing good cache data with instructions prefetched based on a mispredicted branch, prefetching may be halted in response to a weakly weighted prediction in the event of a cache miss.