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Duplex and triple modular redundancy (TMR) systems are used when a high-level of reliability is desired. Real-time systems for autonomous critical missions need such degrees of reliability, but energy consumption becomes a dominant concern when these systems are built from high-performance processors that consume a large budget of electrical power for operation and cooling. Examples where energy consumption and real time are of paramount importance include reliable computers onboard mobile vehicles, such as the Mars Rover, satellites, and other autonomous vehicles. At first inspection, a duplex system uses about two thirds of the components that a TMR system does, leading one to conclude that duplex systems are more energy-efficient. This paper shows that this is not always the case. We present an analysis of the energy efficiency of duplex and TMR systems when used to tolerate transient failures. With no power management deployed, the analysis supports the intuitive impression about the relative superiority of duplex systems in energy consumption. The analysis shows, however that the gap in energy consumption between the two types of systems diminishes with proper power management. We introduce the concept of an optimistic TMR system that offers the same reliability and performance as the traditional one, but at a fraction of the energy consumption budget. Optimistic TMR systems are competitive with respect to energy consumption when compared with a power-aware duplex system, can even exceed it in some situations, and have the added bonus of providing tolerance to permanent faults.