A compressor system for compressing gases in a multistage compression includes a next-to-last compressor in a flow direction and a last compressor which are connected in series, one or more intercoolers between the next-to-last compressor and the last compressor, and an adsorption dryer connected downstream of the last compressor and designed as a rotation dryer having a rotating adsorption chamber. An inside of the adsorption chamber includes a regeneration sector and a drying sector. The regeneration sector is connected to the last compressor such that the compressed gas stream output from the last compressor is guided in a full stream principle through the regeneration sector. A bypass line which bypasses the intercoolers is situated between next-to-last compressor and last compressor, and includes a setting element to set the gas stream guided via the bypass line and therefore the regeneration entry temperature of the compressed gas in the regeneration sector appropriately.