  We introduce a Bayesian method for fitting faint, resolved stellar spectra in
order to obtain simultaneous estimates of redshift and stellar-atmospheric
parameters. We apply the method to thousands of spectra---covering 5160-5280
Angs. at resolution R~20,000---that we have acquired with the MMT/Hectochelle
fibre spectrograph for red-giant and horizontal branch candidates along the
line of sight to the Milky Way's dwarf spheroidal satellite in Draco. The
observed stars subtend an area of ~4 deg^2, extending ~3 times beyond Draco's
nominal `tidal' radius. For each spectrum we tabulate the first four
moments---central value, variance, skewness and kurtosis---of posterior
probability distribution functions representing estimates of the following
physical parameters: line-of-sight velocity v_los, effective temperature
(T_eff), surface gravity (logg) and metallicity ([Fe/H]). After rejecting
low-quality measurements, we retain a new sample consisting of 2813 independent
observations of 1565 unique stars, including 1879 observations for 631 stars
with (as many as 13) repeat observations. Parameter estimates have median
random errors of sigma_{v_los}=0.88 km/s, sigma_{T_eff}=162 K, sigma_logg=0.37
dex and sigma_[Fe/H]=0.20 dex. Our estimates of physical parameters distinguish
~470 likely Draco members from interlopers in the Galactic foreground.
