  A $\sigma$-ideal $\cal{I}$ on a set $X$ is supersaturated if for every family
$\cal{F}$ of $\cal{I}$-positive sets with $|\cal{F}| < \mathrm{add}(\cal{I})$,
there exists a countable set that meets every set in $\cal{F}$. We show that
many well-known ccc forcings preserve supersaturation. We also show that the
existence of supersaturated ideals is independent of ZFC plus "There exists an
$\omega_1$-saturated $\sigma$-ideal".
