We study the energy efficiency benefits of bypassing trivial computations in high-performance processors. Trivial computations are those computations whose output can be determined without performing the computation. We show that bypassing trivial instructions reduces energy consumption while improving performance. Our study shows that by bypassing trivial instructions and for the subset of SPEC'2K benchmarks studied here, on average, it is possible to improve energy and energy-delay by up to 4.5% and 11.8% over a conventional processor.