A computer is provided having a bus interface unit coupled between a CPU bus, a peripheral bus, and a memory bus. The bus interface unit includes a processor controller linked to the CPU bus for controlling the transfer of cycles from the CPU to the peripheral bus and memory bus. Those cycles can be arranged in order within the CPU bus pipeline. A subset of cycles destined for a peripheral bus can be stalled within a snoop phase associated with the CPU bus. Snoop stall can continue until a memory cycle is encountered upon the CPU bus pipeline within a phase prior to the snoop phase. Once the memory cycle progresses to the snoop phase, snoop stall can be discontinued and the previous, peripheral cycles can then be deferred and/or retried, allowing the memory cycle to be quickly dispatched through all phases of the CPU bus and onto the memory bus. In this fashion, memory cycles can be completed quickly, yet deferrals or retries are minimized to avoid the throughput penalty associated with deferring or retrying cycles back again through each phase of the CPU bus.