A microprocessor chip has instruction pipeline circuitry, and instruction classification circuitry that classifies instructions as they are executed into a small number of classes and records a classification code value. An on-chip table has entries corresponding to a range of addresses of a memory and designed to hold a statistical assessment of a value of consulting an off-chip table in a memory of the computer. Lookup circuitry is designed to fetch an entry from the on-chip table as part of the basic instruction processing cycle of the microprocessor. A mask has a value set at least in part by a timer. The instruction pipeline circuitry is controlled based on the value of the on-chip table entry corresponding to the address of instructions processed, the current value of the mask, the recorded classification code, and the off-chip table.