  Fitting Galactic structure models to star counts only provides useful
information about the Galaxy in some directions. In this paper, we investigate
the use of $\chi^2$ goodness-of-fit tests to discriminate between degenerate
Galactic structure models, and the implications of this technique for the
Galactic spheroid and thick disk components. The axis ratio of the Galactic
spheroid and the normalization of spheroid stars with respect to disk stars
introduce a degenerate effect which means that Galactic structure models with
certain combinations of these parameters are indistinguishable from each other
in most directions. We present an analysis of the optimal directions in which
these degeneracies can be lifted. Poisson and magnitude errors are taken into
account, and an attempt is made to place an upper limit on the systematic error
due to separation of spheroid stars from thick/old disk stars. We find that the
magnitude range $20 < V < 21$ is the best for lifting most degeneracies, and
present the optimal combinations of directions using which this can be
achieved. We also give directions in which the signature of the presence of a
Galactic thick disk can be most readily identified, and the directions in which
contamination from a thick disk can be minimized. It is hoped that forthcoming
data from large-scale sky surveys would reveal much about the structure of our
Galaxy using star count techniques.
