An automatic screw machine (20) has a body (22), and a head (21) that is rotatably mounted on the body and that is adapted to be selectively rotated relative to the body between any of a plurality of index positions. The body and head have closely-spaced and facing bearing surfaces (25, 28 and 26, 29), have spindles (23) journalled on the head for rotation relative thereto, and have a source of pressurized lubricant. The improvement broadly includes: at least one body passageway (32) communicating the source with the body bearing surface, the intersection of each body passageway with the body bearing surface defining a body port (33); a head passageway (36) communicating the head bearing surface with the spindle, the intersection of said head passageway with said head bearing surface defining at least one head port (42); and the body and head passageways being so configured and arranged such that lubricant may flow from the source to the spindle only when the head is in the vicinity of the index position such that the body and head ports overlap one another.