This paper presents a precomputation-based guarding technique to reduce both dynamic and static power consumptions in CMOS VLSI circuits. More precisely, a high threshold sleep transistor is placed in series with some portions of the circuit. Based on the input values of the circuit, the sleep transistor is turned on and off, thus, saving both dynamic and static power. We show how to apply this technique to a number of common arithmetic blocks, including comparators, adders and multipliers. Finally, dynamic guarding and sleep transistor activity reduction techniques for improving the performance of the method are presented. Experimental results show 81% reduction in the power consumption of data path modules of a commercial VLIW processor can be achieved using our techniques. This is 20% higher than what has been achieved by previous methods.