A liquid-cooled compressor housing assembly, comprising: a compressor housing comprising a wheel shroud that defines a contour, a diffuser-defining wall joined integrally with the wheel shroud and extending radially outwardly therefrom, and a radially outer wall joined integrally with a radially outermost extent of the diffuser-defining wall, the radially outer wall defining a volute contiguous with the diffuser-defining wall, wherein the wheel shroud, the diffuser-defining wall, and the radially outer wall collectively bound an open-ended cavity that extends into the compressor housing along an axially downstream direction, an upstream end of the cavity being open; and a cover formed as a separate structure from the compressor housing, the cover being affixed to the compressor housing by one or more fastening devices such that the cover closes the open upstream end of the cavity, whereby a coolant passage is defined between and bounded by the cover and the cavity in the compressor housing, wherein the cover includes a peripheral wall encircling a longitudinal axis of the compressor housing assembly, the peripheral wall being received into the cavity in the compressor housing such that the coolant passage is bounded in part by a radially outer surface of the peripheral wall, the peripheral wall defining a radially inner surface comprising an air-guiding surface in use, characterized in that the cover further includes an integrally joined air inlet wall that is spaced radially inwardly from the peripheral wall of the cover, the air inlet wall comprising a radially outer surface that is spaced radially inwardly from the radially inner air-guiding surface of the peripheral wall of the cover so as to define a recirculation passage therebetween, and wherein a bleed port is defined between an upstream end of the wheel shroud and a downstream end of the air inlet wall, the bleed port extending into the recirculation passage. a compressor housing comprising a wheel shroud that defines a contour, a diffuser-defining wall joined integrally with the wheel shroud and extending radially outwardly therefrom, and a radially outer wall joined integrally with a radially outermost extent of the diffuser-defining wall, the radially outer wall defining a volute contiguous with the diffuser-defining wall, wherein the wheel shroud, the diffuser-defining wall, and the radially outer wall collectively bound an open-ended cavity that extends into the compressor housing along an axially downstream direction, an upstream end of the cavity being open; and a cover formed as a separate structure from the compressor housing, the cover being affixed to the compressor housing by one or more fastening devices such that the cover closes the open upstream end of the cavity, whereby a coolant passage is defined between and bounded by the cover and the cavity in the compressor housing, wherein the cover includes a peripheral wall encircling a longitudinal axis of the compressor housing assembly, the peripheral wall being received into the cavity in the compressor housing such that the coolant passage is bounded in part by a radially outer surface of the peripheral wall, the peripheral wall defining a radially inner surface comprising an air-guiding surface in use, characterized in that the cover further includes an integrally joined air inlet wall that is spaced radially inwardly from the peripheral wall of the cover, the air inlet wall comprising a radially outer surface that is spaced radially inwardly from the radially inner air-guiding surface of the peripheral wall of the cover so as to define a recirculation passage therebetween, and wherein a bleed port is defined between an upstream end of the wheel shroud and a downstream end of the air inlet wall, the bleed port extending into the recirculation passage.