A compressor for a gas turbine engine comprising: a rotor having a hub defining a central axis of rotation and a plurality of blades radially extending from the hub to project into an annular gas flow passage of said compressor, each of said blades having a remote blade tip and a leading edge defined between opposed pressure and suction surfaces (48,50), said rotor being rotatable about said axis of rotation; an annular shroud (32;132) circumferentially surrounding the rotor and having a radially inner surface adjacent to the blade tips, the inner surface of the shroud facing said annular gas flow passage; and a plurality of bleed holes (36;136;236) extending through said shroud (32;132) adjacent said blade tips, the bleed holes (36;136;236) providing gas flow communication between said annular gas flow passage and a region outside the shroud (32;132), each of said bleed holes (36;136;236) having an inlet end (33;133) disposed in the radially inner surface of the shroud (32,132) adjacent the blade tips to communicate with the annular gas flow passage, each of said bleed holes (36;136;236) having an outlet end (35;135) disposed in a radially outer surface of the shroud (32;132), bleed air removed from the annular gas flow passage by the bleed holes (36;136;236) flowing from the inlet end (33;133) to the outlet end (35;135) of the bleed holes (36;136;236), characterised in that the outlet end (35;135) of each of said bleed holes (36;136;236) being located circumferentially upstream of the inlet end (33;133) thereof relative to a direction of rotational flow in the annular gas flow passage driven by a direction of rotation of the rotor to bleed off the tip leakage flow. a rotor having a hub defining a central axis of rotation and a plurality of blades radially extending from the hub to project into an annular gas flow passage of said compressor, each of said blades having a remote blade tip and a leading edge defined between opposed pressure and suction surfaces (48,50), said rotor being rotatable about said axis of rotation; an annular shroud (32;132) circumferentially surrounding the rotor and having a radially inner surface adjacent to the blade tips, the inner surface of the shroud facing said annular gas flow passage; and a plurality of bleed holes (36;136;236) extending through said shroud (32;132) adjacent said blade tips, the bleed holes (36;136;236) providing gas flow communication between said annular gas flow passage and a region outside the shroud (32;132), each of said bleed holes (36;136;236) having an inlet end (33;133) disposed in the radially inner surface of the shroud (32,132) adjacent the blade tips to communicate with the annular gas flow passage, each of said bleed holes (36;136;236) having an outlet end (35;135) disposed in a radially outer surface of the shroud (32;132), bleed air removed from the annular gas flow passage by the bleed holes (36;136;236) flowing from the inlet end (33;133) to the outlet end (35;135) of the bleed holes (36;136;236), characterised in that the outlet end (35;135) of each of said bleed holes (36;136;236) being located circumferentially upstream of the inlet end (33;133) thereof relative to a direction of rotational flow in the annular gas flow passage driven by a direction of rotation of the rotor to bleed off the tip leakage flow.