A family of subsets of [n] is called s-saturated if it contains no s pairwise disjoint sets, and moreover, no set can be added to while preserving this property. More than 40 years ago, Erdős and Kleitman conjectured that an s-saturated family of subsets of [n] has size at least . It is a simple exercise to show that every s-saturated family has size at least , but, as was mentioned by Frankl and Tokushige, even obtaining a slightly better bound of , for some fixed , seems difficult. We prove such a result, showing that every s-saturated family of subsets of [n] has size at least . In this talk, I will present two short proofs. This is joint work with M. Bucic, S. Letzter and B. Sudakov.