  We investigate the stability of stars with a density discontinuity between a
high-density core and a very low density mantle. Previous work on "strange
dwarfs" suggested that such a discontinuity could stabilize stars that would
have been classified as unstable by the conventional criteria based on extrema
in the mass-radius relation. We investigate the stability of such stars by
numerically solving the Sturm-Liouville equations for the lowest-energy modes
of the star. We find that the conventional criteria are correct, and strange
dwarfs are not stable.
