Abstract: A bridge for interfacing buses in a computer system having an industry standard architecture (ISA) bus and a peripheral controller interconnect (PCI) bus is coupled between the ISA and PCI buses. Devices coupled to the buses are either PCI bus-compliant devices or are non-PCI bus-compliant devices. A power management device in the computer system is able to place the computer system into a low power suspend mode, a resume mode and an active mode. The bridge has a multi-tiered arbitration device for arbitrating among the PCI bus-compliant devices and the non-PCI bus-compliant devices for control of the computer system. The arbitration device is responsive to the power management device to controllably suspend arbitration when the power management device indicates that the suspend mode is being entered.