A compressed-air compressor for producing compressed air for a compressed-air system of a vehicle includes a cylinder and a piston. The piston is arranged in the cylinder and divides the interior space of the cylinder into a compression chamber, which can be connected to the compressed-air system of the vehicle for the purpose of conveying compressed air, and a neutral chamber. The neutral chamber is charged with an auxiliary pressure such that the pressure in the neutral chamber is temporally on average higher than atmospheric pressure. The compressed air production using the piston/cylinder-type compressed-air compressor is improved such that the maximum value of the torque to be imparted for driving the compressor is reduced.