A criterion fails to be necessary for ontological commitment if it undergenerates, if it sometimes fails to hold that a theory is committed to some kind of entity that the theory should be committed to. Quantifier criteria will undergenerate if they fail to account for all the implicit ontological commitments of theories. Whereas the problems canvassed in §1.6 for the sufficiency of a quantifier account can all be addressed by a devoted Quinean, the problems with necessity are more serious. Indeed, they suggest that Quinean approaches that focus on the values of the variables of quantification should be jettisoned for a more general entailment approach to ontological commitment (§2).