A method and apparatus for arbitrating between command streams. The method unblocks high priority commands which are blocked and then selects any remaining high priority commands. Normal priority commands are selected after the high priority commands. A memory controller described includes a command queue block having a plurality of command queues, each being coupled to receive a different type of command. The memory controller also includes arbitration logic which, among other things, selects high priority read commands before high priority write commands. Memory interface logic generates memory accesses performing commands selected by the arbitration logic.