A method for operating a packaged terminal air conditioner includes activating a compressor of the packaged terminal air conditioner such that refrigerant flows through an interior coil of the packaged terminal air conditioner, and, while the compressor is active, periodically cycling a fan of the packaged terminal air conditioner between a low speed active operating state and an inactive operating state. The fan runs at a modulated speed limit of the fan in the low speed active operating state, and the fan is unpowered in the inactive operating state.