  This paper addresses available constraints on mass models fitted to rotation
curves. Mass models of disk galaxies have well-known degeneracies, that prevent
a unique mass decomposition. The most notable is due to the unknown value of
the stellar mass-to-light ratio (the disk-halo degeneracy); even with this
known, degeneracies between the halo parameters themselves may prevent an
unambiguous determination of the shape of the dark halo profile, which includes
the inner density slope of the dark matter halo. The latter is often referred
to as the ``cusp-core degeneracy''. We explore constraints on the disk and halo
parameters and apply these to four mock and six observed disk galaxies with
high resolution and extended rotation curves. Our full set of constraints
consists of mass-to-light (M/L) ratios from stellar population synthesis models
based on B-R colors, constraints on halo parameters from N-body simulations,
and constraining the halo virial velocity to be less than the maximum observed
velocity. These constraints are only partially successful in lifting the
cusp-core degeneracy. The effect of adiabatic contraction of the halo by the
disk is to steepen cores into cusps and reduce the best-fit halo concentration
and M/L values (often significantly). We also discuss the effect of disk
thickness, halo flattening, distance errors, and rotation curve error values on
mass modeling. Increasing the imposed minimum rotation curve error from
typically low, underestimated values to more realistic estimates decreases the
chi-square substantially and makes distinguishing between a cuspy or cored halo
profile even more difficult. In spite of the degeneracies and uncertainties
present, our constrained mass modeling favors sub-maximal disks (i.e., a
dominant halo) at 2.2 disk scale lengths, with Vdisk/Vtot < 0.6.
