A technique for invoking a low power operational mode in response to a halt instruction is used in a computer system that includes a processor coupled to external logic. The processor includes at least (i) a pipeline subcircuit to execute programmed instructions, including halt instructions, (ii) an interrupt handling subcircuit to handle interrupts generated by external interrupt logic, and (iii) clock generator circuitry that supplies clock signals to the pipeline and interrupt handling subcircuits. In response to execution of a halt instruction, the processor (i) enters the low power operational mode in which power consumption is reduced at least for the pipeline subcircuit, but without stopping the supply of clock signals to the interrupt handling subcircuit, and (ii) generates an acknowledgement signal to the external logic indicating that the clock signals to the pipeline subcircuit are being stopped, thereby entering the low power operational mode. In a preferred embodiment, the low power operational mode is entered by stopping the clock generator circuitry from supplying clock signals to the pipeline subcircuit, but not to the interrupt handling subcircuit. To resume normal processing, the interrupt handling subcircuit responds to an interrupt generated by the external logic by causing the clock generator circuitry to resume supplying clock signals to the pipeline subcircuit.