A bleed air cooling system for a gas turbine engine includes one or more bleed flowpaths operably connected to a bleed outlet to divert a bleed airflow from a gas turbine engine flowpath. Each bleed flowpath includes two or more bleed ports to divert a bleed airflow from a gas turbine engine flowpath, a bleed duct configured to convey the bleed airflow from the two or more bleed ports to the bleed outlet, and a delta-pressure valve located at each bleed port of the two or more bleed ports configured to move between an opened position and a closed position in response to a difference between a first pressure upstream of the delta-pressure valve and a second pressure downstream of the delta pressure valve. The bleed airflow is selectably conveyed through a bleed port of the two or more bleed ports depending on the operation of the associated delta-pressure valve.