  We show that an unambiguous and correct quantization of the second-class
constrained system of a free particle on a sphere in $D$ dimensions is possible
only by converting the constraints to abelian gauge constraints, which are of
first class in Dirac's classification scheme. The energy spectrum is equal to
that of a pure Laplace-Beltrami operator with no additional constant arising
from the curvature of the sphere. A quantization of Dirac's modified Poisson
brackets for second-class constraints is also possible and unique, but must be
rejected since the resulting energy spectrum is physically incorrect.
