  We examine potential deformations of inner black hole and cosmological
horizons in Reissner-Nordstr\"om de-Sitter spacetimes. While the rigidity of
the outer black hole horizon is guaranteed by theorem, that theorem applies to
neither the inner black hole nor past cosmological horizon. Further for pure
deSitter spacetime it is clear that the cosmological horizon can be deformed
(by translation). For specific parameter choices, it is shown that both inner
black hole and cosmological horizons can be infinitesimally deformed. However
these do not extend to finite deformations. The corresponding results for
general spherically symmetric spacetimes are considered.
