One important way to reduce power consumption is to reduce the spurious switching activity in a circuit or circuit component, i.e., activity that is not required by its specified functionality. Given a scheduled behavior and functional unit binding, we show that spurious switching activity can be reduced through proper register binding using retentive multiplexers. Retentive multiplexers can preserve their previous select signal values in the control steps in which the select signals are don't cares. A functional unit, in which spurious switching activity is completely eliminated, is called perfectly power managed. We present a general sufficient condition for register binding to ensure a set of functional units to be perfectly power managed. This condition not only applies to data-flow intensive behaviors, but also to control-flow intensive behaviors. It leads to a straightforward power-managed (PM) register-binding algorithm, which uses this condition to preserve the previous values in the input registers of a functional unit during the states in which the unit is idle. The proposed algorithm is general and independent of the functional unit binding and scheduling algorithms. Hence, it can be easily incorporated into existing high-level synthesis systems. For the benchmarks we experimented with, an average 40.7% power reduction was achieved by our method at the cost of 6.9% average area overhead, compared to power-optimized register-transfer level circuits, which did not use PM register binding.