A method of controlling operation of a pair of two-stage air conditioners. The method monitors a temperature of an area served by the air conditioners; activates a first stage of a first or lead air conditioner when the temperature rises above a first set point temperature; activates a first stage of a second or lag air conditioner when the temperature rises above a second set point temperature; activates a second stage of the first air conditioner only if the temperature remains above the second set point temperature beyond a first selected time period; and activates a second stage of the second air conditioner only if the temperature remains above the second set point temperature beyond a second selected time period. Neither of the air conditioners is operated in their less efficient second stages if both air conditioners are not first operating in their high efficiency first stages so that the entire cooling requirements of the area served by the air conditioners is primarily served by the first high efficiency stage of one or both the air conditioners.