A compressor section for a gas turbine engine comprising: at least one stage of rotor blades (64a-64e) extending circumferentially around a center axis; and a compressor case comprising: an annular body that extends circumferentially around the at least one stage of rotor blades (64a-64e) and extends axially along the center axis, wherein the annular body has an inner surface and an outer surface; a first bleed manifold formed axially forward of the at least one stage of rotor blades (64a-64e); a second bleed manifold formed axially aft of the first bleed manifold; a bleed inlet extending through the annular body and into the first bleed manifold; and cooling passages formed in the annular body; wherein the first bleed manifold encloses a first plenum and the second bleed manifold encloses a second plenum, wherein each of the cooling passages extends from the first plenum to the second plenum and fluidically connects the first plenum to the second plenum, characterised in that: the cooling passages are radially between the inner surface and the outer surface of the annular body; and each of the first bleed manifold and second bleed manifold are formed on the outer surface of the annular body. at least one stage of rotor blades (64a-64e) extending circumferentially around a center axis; and a compressor case comprising: an annular body that extends circumferentially around the at least one stage of rotor blades (64a-64e) and extends axially along the center axis, wherein the annular body has an inner surface and an outer surface; a first bleed manifold formed axially forward of the at least one stage of rotor blades (64a-64e); a second bleed manifold formed axially aft of the first bleed manifold; a bleed inlet extending through the annular body and into the first bleed manifold; and cooling passages formed in the annular body; wherein the first bleed manifold encloses a first plenum and the second bleed manifold encloses a second plenum, wherein each of the cooling passages extends from the first plenum to the second plenum and fluidically connects the first plenum to the second plenum, characterised in that: the cooling passages are radially between the inner surface and the outer surface of the annular body; and each of the first bleed manifold and second bleed manifold are formed on the outer surface of the annular body. an annular body that extends circumferentially around the at least one stage of rotor blades (64a-64e) and extends axially along the center axis, wherein the annular body has an inner surface and an outer surface; a first bleed manifold formed axially forward of the at least one stage of rotor blades (64a-64e); a second bleed manifold formed axially aft of the first bleed manifold; a bleed inlet extending through the annular body and into the first bleed manifold; and cooling passages formed in the annular body; wherein the first bleed manifold encloses a first plenum and the second bleed manifold encloses a second plenum, wherein each of the cooling passages extends from the first plenum to the second plenum and fluidically connects the first plenum to the second plenum, characterised in that: the cooling passages are radially between the inner surface and the outer surface of the annular body; and each of the first bleed manifold and second bleed manifold are formed on the outer surface of the annular body.