A parison mold assembly for a press-and-blow glassware forming machine includes a neck ring for molding a finish portion of a parison, a parison mold for molding a body portion of the parison, and a plunger for insertion through the neck ring into the parison mold for pressing a hot glass gob against inner surfaces of the neck ring and the parison mold. The plunger has an outer surface of revolution around a central axis, including a first portion disposed within the neck ring when the plunger is fully inserted through the neck ring into the parison mold, a second portion spaced from the first portion, and a transition third portion extending between the first and second portions.