  We have analysed HST/WFPC2 F555W and F814W images for fifteen elliptical
galaxies with kinematically-distinct cores. For each of them we have derived
surface brightness and isophotal parameter profiles in the two bands, color
maps, and radial profiles in (V-I). We have detected photometric evidence for
faint stellar disks, on scales of a few tens to a few arcseconds, in seven
galaxies, namely NGC 1427, 1439, 1700, 4365, 4406, 4494 and 5322. In NGC 1700,
the isophotes are slightly boxy at the scale of the counter-rotating component,
and disky at larger radii. We find no difference in (V-I) color greater than
0.02 mag between these disks and the surrounding galactic regions. Hence the
stellar populations in the kinematically distinct cores are not strongly
deviant from the population of the main body. For one galaxy, NGC 4365, the
innermost region is bluer than the surrounding regions. This area extends to
about 15pc, and contains a luminosity of 2.5x10^6 L$_\odot$. If interpreted as
a stellar population effect, an age difference of $\sim$ 3-4 Gyrs, or an
$[Fe/H]$ variation of about 0.2 dex, is derived. The nuclear intensity profiles
show a large variety: some galaxies have steep cusp profiles, others have
shallow cusps and a ``break radius''. The nuclear cusps of galaxies with
kinematically-distinct cores follow the same trends as the nuclei of normal
galaxies. We have not been able to identify a unique, qualifying feature in the
WFPC2 images which distinguish the galaxies with kinematically distinct cores
from the kinematically normal cores. [shortened]
