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We present projected velocity dispersion profiles for the Draco and UrsaMinor (UMi) dwarf spheroidal galaxies based on 207 and 162 discrete stellarvelocities, respectively. Both profiles show a sharp decline in the velocitydispersion outside ~30 arcmin (Draco) and ~40 arcmin (UMi). New, deepphotometry of Draco reveals a break in the light profile at ~25 arcmin. Thesedata imply the existence of a kinematically cold population in the outer partsof both galaxies. Possible explanations of both the photometric and kinematicdata in terms of both equilibrium and non-equilibrium models are discussed indetail. We conclude that these data challenge the picture of dSphs as simple,isolated stellar systems.Comment: 5 pages, accepted for publication in ApJ Letter

Kinematically Cold Populations at Large Radii in the Draco and Ursa Minor Dwarf Spheroidal Galaxies