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Combustion in conventional fossil-fueled power plants is highly irreversible, resulting in poor overall energy conversion efficiency values (less than 40 percent in many cases). The objective of this paper is to discuss means by which this combustion irreversibility might be reduced in gas turbine power cycles, and the conversion efficiency thus improved upon. One such means is thermochemical recuperation of exhaust heat. The proposed cycle recycles part of the exhaust gases, then mixes them with fuel prior to injection into a reformer. The heat required for the endothermic reforming reactions is provided by the hot turbine exhaust gases. Assuming state-of-the-art technology, and making a number of simplifying assumptions, an overall efficiency of 65.4 percent was attained for the cycle, based on the lower heating value (LHV) of the methane fuel. The proposed cycle is compared to a Humid Air Turbine (HAT) cycle with similar features that achieves an overall efficiency of 64.0 percent. The gain in cycle efficiency that can be attributed to the improved fuel oxidation process is 1.4 percentage points. Compared to current high-efficiency gas turbine cycles, the high efficiency of both cycles studied therefore results mainly from the use of staged compression and expansion with intermediate cooling and reheating, respectively.