An optimized CO2 air-conditioning system for a vehicle has individual components designed and/or matched to one another in such a way that if the high pressures in the high-pressure section deviate by up to ±30% from the optimum high pressures, the associated optimum performance figures are reduced by no more than 20%. The individual components include a controllable compressor, a gas cooler, an internal heat exchanger, an evaporator and an accumulator. As a result, a fixed throttle expansion member can be used between the high-pressure and low-pressure sections of the system.