Structure and method are provided for reducing power consumption in a computer system without sacrificing computer performance or inhibiting a computer user's rapid access to the computer. An identifier, such as a device address, network address, serial number, and the like, is associated with each device or resource. Communications over a communications link such as a parallel bus, serial bus, or wireless link, are monitored by each device to determine device identifiers communicated over the link, and these identifiers are compared to the identifier associated with the monitoring device. Each device monitors the communications and is responsible for self-controlling its operating condition to minimize power consumption. Each device includes a first component which operates continuously to provide the monitoring function, and a second component that operates in a low power consumption mode unless the first component signals the second component that its operation is needed during that time period. Typically, the first component withholds a device operating input, for example a clock signal, from the second component when none of the communicated identifiers match the particular device; and provide the operating input when one matches. In the first component, the number of circuit elements is reduced so that the number of circuit elements which are continuously active are reduced. The structure and method provide very fine temporal control of power consumption in the computer system.