In fault tolerance for parallel and distributed systems, message logging protocols have played a prominent role in the last three decades. Such protocols enable local rollback to provide recovery from fail-stop errors. Global rollback techniques can be straightforward to implement but at times lead to slower recovery than local rollback. Local rollback is more complicated but can offer faster recovery times. In this work, we study the power and energy efficiency implications of global and local rollback. We propose a power-efficient version of local rollback to reduce power consumption for non-critical, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">blocked</i> processes, using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Dynamic Voltage and Frequency Scaling</i> (DVFS) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">clock modulation</i> (CM). Our results for 3 different MPI codes on 2 parallel systems show that power-efficient local rollback reduces CPU energy waste up to 50% during the recovery phase, compared to existing global and local rollback techniques, without introducing significant overheads. Furthermore, we show that savings manifest for all blocked processes, which grow linearly with the process count. We estimate that for settings with high recovery overheads the total energy waste of parallel codes is reduced with the proposed local rollback.