  (Abridged) We use N-body simulations to explore the effects of tidal
stripping on the structure of dwarf spheroidal galaxies (dSphs). We model dSphs
as King spheres embedded in NFW dark halos that orbit the Galactic potential on
eccentric orbits. We find that episodes of stellar mass loss remove the initial
cutoff of the bound stellar core. Once equilibrium has been re-established the
outer mass profile approaches a power-law in projection that is well described
by a simple Plummer model. Tides also result in transient features in the outer
density profile. As the system re-equilibrates, an outward-moving "excess" of
stars is found at radii where the local crossing time exceeds the time elapsed
since pericenter. If the orbit is known, these results provide a simple way to
assess whether "breaks" and "bumps" in the profile of dSphs are actually tidal
in origin. We apply this to the Sagittarius dwarf and, encouragingly, identify
two features in the profile that may be traced to its two last pericentric
passages. Applied to Leo I, we find that any tidal break would locate beyond
the area surveyed by current data, casting doubt on recent claims of the
detection of tidal debris around this galaxy. For Carina, the tidal break
should occur at a radius twice farther than observed, suggesting that the outer
excess of stars is not tidal in origin unless its orbit is in error. A similar
comment applies to Sculptor, whose pericenter appears too large for Galactic
tides to be important but whose outer profile, like that of Draco, nonetheless
follows closely a Plummer-law. Fornax and Leo II show no sign of a power-law
outer profile, suggesting that they have not suffered stellar tidal stripping.
Published profiles for other, fainter Milky Way dSph companions do not extend
sufficiently far to allow for conclusive assessment.
