An integral domain
$D$
with identity is condensed (resp., strongly condensed) if for each pair of ideals
$I,\,J$
of
$D,\,IJ\,=\,\{ij\,;\,i\,\in I,j\in J\,\}$
(resp.,
$IJ=iJ$
for some
$i\,\in \,I$
or
$IJ\,=Ij$
for some
$j\,\in \,J$
). We show that for a Noetherian domain
$D,\,D$
is condensed if and only if
$\text{Pic}\left( D \right)\,=0$
and
$D$
is locally condensed, while a local domain is strongly condensed if and only if it has the two-generator property. An integrally closed domain
$D$
is strongly condensed if and only if
$D$
is a Bézout generalized Dedekind domain with at most one maximal ideal of height greater than one. We give a number of equivalencies for a local domain with finite integral closure to be strongly condensed. Finally, we show that for a field extension
$k\,\subseteq K$
, the domain
$D=\,k+XK[[X]]$
is condensed if and only if
$[K:k]\,\le \,2$
or
$[K:k]\,=\,3$
and each degree-two polynomial in
$k[X]$
splits over
$k$
, while
$D$
is strongly condensed if and only if
$[K:k]\,\le \,2$
.