  We present a detailed morphological, photometric, and kinematic analysis of
two barred S0 galaxies with large, luminous inner disks inside their bars. We
show that these structures, in addition to being geometrically disk-like, have
exponential profiles (scale lengths $\sim$ 300--500 pc) distinct from the
central, non-exponential bulges. We also find them to be kinematically
disk-like. The inner disk in NGC 2787 has a luminosity roughly twice that of
the bulge; but in NGC 3945, the inner disk is almost ten times more luminous
than the bulge, which itself is extremely small (half-light radius $\approx$
100 pc, in a galaxy with an outer ring of radius $\approx$ 14 kpc) and only
$\sim$ 5% of the total luminosity -- a bulge/total ratio much more typical of
an Sc galaxy. We estimate that at least 20% of (barred) S0 galaxies may have
similar structures, which means that their bulge/disk ratios may be
significantly overestimated. These inner disks dominate the central light of
their galaxies; they are at least an order of magnitude larger than typical
``nuclear disks'' found in ellipticals and early-type spirals. Consequently,
they must affect the dynamics of the bars in which they reside.
