We consider the question: when does a $\Psi$-space satisfy property (a)? We show that if ${\cal A}$ is an almost disjoint family of infinte subsets of the integers and $|{\cal A}| < \frak{p}$ then the $\Psi$-space $\Psi({\cal A})$ satisfies property (a) but in some Cohen models where the negation of the continuum hypothesis holds, every uncountable $\Psi$-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller, there exists a $\Psi$-space of cardinality $\frak{p}$ which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).