A computer system including an instruction cache (I-cache) having a plurality of banks for storing a subset of data from memory is shown to include a prediction mechanism for predicting which bank of the I-cache contains the required data. A prediction value, including a sequential prediction hint and a branch prediction hint, is associated with each instruction stored in the I-cache. The prediction value may either be stored with the I-cache data, or in a separate memory included before the I-cache. If the predicted value is incorrect, the predicted hint is `trained` to provide a higher degree of accuracy for repetitive instruction stream operation. Processor performance is additionally improved by providing a branch hint that allows for smoother transition between changing instruction streams.