We present a design strategy to reduce power demands in application-specific, heterogeneous multiprocessor systems with interdependent subtasks. This power reduction scheme can be used with a randomised search such as a genetic algorithm where multiple trial solutions are tested. The scheme is applied to each trial solution after allocation and scheduling have been performed. Power savings are achieved by equally expanding each processor's execution time with a corresponding reduction in their respective operating voltage. Lowest cost solutions achieve average reductions of 24% while minimum power solutions average 58%.