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In this paper, we discuss the use of a 3rd harmonic component to the drive voltage on the grid of an inductive output tube (IOT). High-efficiency inductive output tubes (IOTs) are typically characterized by efficiencies up to 70 - 75%. However, the achievement of efficiencies greater than 80% would substantially reduce the operating costs of next-generation accelerators. In order to achieve this goal, we consider the addition of a 3rd harmonic component to the drive signal on the grid of an inductive output tube. The use of a 3rd harmonic drive component in IOT guns has been considered in order to apply such a gun as the injector [1] of radio frequency linear accelerators (RF linacs). Here we consider that the IOT will be used to provide the rf power to drive RF linacs and apply the 3rd harmonic with the intention of increasing the efficiency of the RF output of the IOT. We consider a model IOT with a 700 MHz resonant cavity and using an annular beam with a voltage of 30 kV, an average current of 6.67 A yielding a perveance of about 1.3e-6 P. We simulate this IOT using the NEMESIS simulation code [2] which has been successfully validated by comparison with the K5H90W-2 IOT developed by Communications and Power Industries. It is found that the effect of the 3rd harmonic on the efficiency is greatest when the phase of the 3rd harmonic is shifted by pi radians with respect to the fundamental drive signal and with 3rd harmonic powers greater than about 50% that of the fundamental drive power. For the present example, we show that efficiencies approaching 86% are possible by this means.