1. In a data processing system comprising: data processor means for executing instructions and for responding to interrupt requests; subsystem means for providing interrupt requests to said data processor; interrupt mask means responsive to the execution of instructions by said data processor means for preventing sid data processor means for responding to interrupt requests from said subsystem means; and clock means for supplying clocking pulses to said data processor means and said subsystem means; a power reduction system comprising: wait mode means responsive to a power-down signal received from said data processor means for reducing power consumption by the data processing system; and clock stopping means responsive to said power-down signal for interrupting the supply of clocking pulses to said subsystem means only if said interrupt mask means is preventing said data processor means from responding to interrupt requests from said subsystem means.