A connector axial compression tool having a lever end and a cable end, with a body slidably supporting a cradle in a cavity formed in the body. The cradle is slidable via a handle which pivots about the body, linked to the cradle by a lever mechanism. The cradle has a shoulder clamp adapted to mate with a connector body. Operation of the handle moves the cradle towards and away from a cable end of the cavity, against a cable clamp through which the cable may pass but against which a cable clamp sleeve of the connector abuts, axially compressing the connector to couple it to the cable. Because the shoulder clamp holds the connector body rather than pressing against the connector interface, a wide range of different connectors may be used with the same tool, without causing damage to the connector interface of the various connectors.