  This is the first of two papers presenting a detailed examination of
Fokker-Planck models for the globular cluster NGC 6397. I show that these
models provide a good match to observations of the surface density profile,
mass functions at three radii and the velocity dispersion profile. The
constraint of requiring the best matches to the mass functions and surface
density profiles to occur simultaneously defines a surface in an initial
parameter space consisting of the cluster concentration, mass, and limiting
radius. I discuss various techniques for locating this surface and the
dependence of the quality of the matches on the position of the model on the
surface, the initial mass function and the retention rate of neutron stars. The
quality of the matches are usually strongly related to the age of the models,
but one initial mass function was found for which the quality of the matches
are independent of time.
