A weld-on female casing connector is disclosed having an upper threaded section and a lower cylindrical section that is welded to the casing. Located between the two sections is a connecting section that has a downwardly decreasing cross-sectional area until the cross-sectional area approaches the cross-sectional area of an ideal transition section and has a stress in the range of other high stress sections of the connector than an increasing cross-sectional area until the outside diameter of the connecting section is sufficient to provide a downwardly facing elevator shoulder of sufficient area to support the casing on an elevator.