  The minimal geometric deformation approach is employed to show the existence
of brane-world stellar distributions with vacuum Schwarzschild exterior, thus
without energy leaking from the exterior of the brane-world star into the extra
dimension. The interior satisfies all elementary criteria of physical
acceptability for a stellar solution, namely, it is regular at the origin, the
pressure and density are positive and decrease monotonically with increasing
radius, finally all energy conditions are fulfilled. A very thin solid crust
with negative radial pressure separates the interior from the exterior, having
a thickness $\Delta $ inversely proportional to both the brane tension $\sigma
$ and the radius $R$ of the star, i.e. $\Delta ^{-1}\sim R\,\sigma $. This
brane-world star with Schwarzschild exterior would appear only thermally
radiating to a distant observer and be fully compatible with the stringent
constraints imposed on stellar parameters by observations of gravitational
lensing, orbital evolutions or properties of accretion disks.
