preforms with a neck region and a preform body and having an enlarged geometry in comparison with the cavity of the injection mould are produced by injecting a polymer melt into the mould with a geometry of the cavity in the mould such that the radial extent of an inner space in the preform body thereby produced is not greater than the radial extent of the inner space in the neck region , the preforms are removed from the open mould by a removal gripper , and the preforms in the removal gripper are inflated using positive pressure such that the geometry of the inflated preform body is larger than the cavity in the injection mould .