A control methodology for dynamically adjusting the switching limits of a cycled refrigerant compressor in an air conditioning system with the objective of achieving an optimal or specified tradeoff between compressor cycling frequency and discharge air temperature variation under all operating conditions. In a first embodiment, the compressor cycling limits are controlled to maintain a virtually constant discharge air temperature variation for all operating conditions. In a second embodiment, the compressor cycling limits are controlled so that the discharge air temperature variation changes in relation to the discharge air temperature to provide a virtually constant human comfort level for the occupants. And in a third embodiment, the compressor cycling limits are controlled so that the discharge air temperature variation changes in relation to the ambient or outside air temperature to provide a virtually constant human comfort level for the occupants.