  We present surface photometry for the central regions of a sample of 33
early-type (E, S0, and S0/a) galaxies observed at 1.6 microns (H band) using
the Hubble Space Telescope (HST). We employ a new technique of two-dimensional
fitting to extract quantitative parameters for the bulge light distribution and
nuclear point sources, taking into consideration the effects of the
point-spread function. Parameterizing the bulge profile with a ``Nuker'' law,
we confirm that the central surface-brightness distributions largely fall into
two categories, each of which correlates with the global properties of the
galaxies. ``Core'' galaxies tend to be luminous ellipticals with boxy or pure
elliptical isophotes, whereas ``power-law'' galaxies are preferentially lower
luminosity systems with disky isophotes. Unlike most previous studies, however,
we do not find a clear gap in the distribution of inner cusp slopes; several
objects have inner cusp slopes (0.3 < gamma < 0.5) which straddle the regimes
conventionally defined for core and power-law type galaxies. The nature of
these intermediate objects is unclear. We draw attention to two objects in the
sample which appear to be promising cases of galaxies with isothermal cores
that are not the brightest members of a cluster. Unresolved nuclear point
sources are found in about 50% of the sample galaxies, roughly independent of
profile type, with magnitudes in the range m^{nuc}_H = 12.8 to 17.4 mag, which
correspond to M_H^{nuc} = -12.8 to -18.4 mag. (Abridged)
