A latchset comprises a latch cam hub configured to rotate on a door handle tailpiece, a first and optionally also a second projection extending radially outward from the hub, a sliding actuator comprising an elongated body and a first tooth, and a spring that resists retraction of the sliding actuator and urges the first projection against the first tooth. The latch cam is operative to retract the sliding actuator when a coupled door handle is rotated in only one rotational direction, such that rotation of the coupled door handle in the opposite rotational direction is inoperative to retract the sliding actuator. The hub is configured to be rotated by 90° during installation to set the latch cam to operate in an oppositely handed door. The latch cam prevents lost motion in eight door configurations.