  We present projected velocity dispersion profiles for the Draco and Ursa
Minor (UMi) dwarf spheroidal galaxies based on 207 and 162 discrete stellar
velocities, respectively. Both profiles show a sharp decline in the velocity
dispersion outside ~30 arcmin (Draco) and ~40 arcmin (UMi). New, deep
photometry of Draco reveals a break in the light profile at ~25 arcmin. These
data imply the existence of a kinematically cold population in the outer parts
of both galaxies. Possible explanations of both the photometric and kinematic
data in terms of both equilibrium and non-equilibrium models are discussed in
detail. We conclude that these data challenge the picture of dSphs as simple,
isolated stellar systems.
