A criterion fails to be sufficient for ontological commitment if it overgenerates, if it sometimes holds that a theory is committed to some kind of entity that the theory should not be committed to. I suppose that any quantifier criterion introduces some sort of entailment relation between theories and existence claims, an entailment relation that depends upon the values of the bound variables of the sentences of the theory.  (That's what distinguishes “quantifier accounts” from the broader “entailment accounts” to be discussed in §2.) Now ask: How could a theory entail that Ks exist without being ontologically committed to Ks? How could the sufficiency of the quantifier criterion fail to be entirely trivial? Is there room to deny that existential consequences of a theory, as given by sentences of first-order logic with the existential quantifier, do not amount to ontological commitments of the theory? Four ways that one might challenge sufficiency will be considered. The first two require only clarifications or minor adjustments to a quantifier criterion. The third and fourth, however, raise philosophically substantial issues.