A high voltage connector, such as one that carries current at a voltage of at least one kilovolts, is constructed to minimize partial discharge (a small amount of current flow) out of locations where a cable conductor has been crimped to the rear of a contact, which resulted in sharp points or edges. A shroud is mounted around the connector, which includes a cylindrical shroud sleeve lying around the crimped region of the contact, with the rear end of the shroud sleeve having rounded edges or abutting a rear shroud element, and with the front end of the shroud preferably being of hemispheric shape.