  We investigate the potential of a future supernova dataset, as might be
obtained by the proposed SNAP satellite, to discriminate among different ``dark
energy'' theories that describe an accelerating Universe. We find that many
such models can be distinguished with a fit to the effective
pressure-to-density ratio, $w$, of this energy. More models can be
distinguished when the effective slope, $dw/dz$, of a changing $w$ is also fit,
but only if our knowledge of the current mass density, $\Omega_m$, is improved.
We investigate the use of ``fitting functions'' to interpret luminosity
distance data from supernova searches, and argue in favor of a particular
preferred method, which we use in our analysis.
