Abstract: A wrench of either a socket or closed-end type is disclosed as including a closed wrench opening (30, 30a, 30', 130, 130a, 130', 230, 230') having curved engagement surfaces that connect associated pairs of flat surfaces. The curved engagement surfaces engage a conventionally toleranced hexagonal fastener without any engagement thereof by the flat surfaces. In one embodiment, the wrench opening (30, 30a, 30', 230) has a "six-point" construction including six circumferentially extending flat surfaces and six pairs of angularly oriented flat surfaces. In another "twelve-point" embodiment, the wrench opening (130, 130a, 130', 230) has twelve pairs of angularly oriented flat surfaces connected by the curved engagement surfaces. Connecting surfaces of the wrench opening connect the flat surfaces in both the "six-point" and "twelve-point" versions.