A tooling for injection-molding a part, the tooling including two cavity blocks each including a cavity formed therein of a shape corresponding to a shape of a part that is to be molded once the cavity blocks have been superposed. At least one of the cavity blocks includes a mechanism for positioning a core, which mechanism includes at least one bearing surface for bearing against the core and at least one presser screw screwed into a threaded passage of the cavity block for purpose of holding the core in position against the bearing surface. The tooling further includes a force-limiter limiting force applied to the core by the presser screw.