Given a (finite) set $S$ of (finite) sets such that $\bigcap S = \emptyset$, how can I find all the smallest subsets $S' \subseteq S$ such that $\bigcap S' = \emptyset$?

Of course, I could just iterate over all the subsets of $S$ (that would be $\mathcal{O}(2^{\left | S \right |})$), but is there a better way to do it?