A computer system has a processor bus under control of the microprocessor itself, and this bus communicates with main memory, providing high-performance access for most cache fill operations. In addition, the system includes one or more expansion buses, preferably of the PCI type in the example embodiment. A host-to-PCI bridge is used for coupling the processor bus to the expansion bus. Other buses may be coupled to the PCI bus via PCI-to-(E) ISA bridges, for example. The host-to-PCI bridge contains queues for posted writes and delayed read requests. All transactions are queued going through the bridge, upstream or downstream. The system bus is superpipelined, in that transactions overlap. A fast burst transactions are allowed between the bridge and main memory, i.e., requests which can be satisfied without deferring or retrying are applied to the system bus without waiting to get a response from the target. A range of addresses (e.g., system memory addresses) is defined to be a fast burst range, and any address in this range is treated differently compared to addresses outside the range. The bridge is programmed, by configuration cycles, to establish this fast burst range, within which it is known that an out-of-order response will not be received. When a transaction reaches a bridge interface from the PCI bus, and it is recognized that the address is within the fast burst range, then the fast burst mode is allowed, and write or read requests can be issued without waiting for the snoop phase, since there is no possibility of defer or retry.