A machine for compression molding plastic closures includes a support mounted for rotation around an axis, and a plurality of compression molds on the support at angularly spaced positions around the axis. Each of the molds includes a male mold section and a female mold section, at least one of which is movable with respect to the other between a closed position to form a compression mold cavity and an open position spaced from each other. The male mold section includes a mold core and a stripper sleeve surrounding the mold core for movement both rotationally and axially of the mold core. A first screw drive couples the female mold section to the stripper sleeve for rotating the stripper sleeve around the mold core as the at least one mold section is moved between the closed and open positions. A second screw drive couples the stripper sleeve to the support to move the stripper sleeve axially over the mold core as the stripper sleeve is rotated around the core. The stripper sleeve thus rotationally and axially removes a closure shell molded around the core as the at least one mold section is moved with respect to the other from the closed toward the open position.