  We parametrize phenomenologically possible new physics effects and calculate
their influence on the invariant dilepton mass spectrum and the Dalitz plot for
the decays $B \to K \ell^+ \ell^-$ and $B \to K^\ast \ell^+ \ell^-$. Especially
the decay into $K^*$ yields a wealth of new information on the form of the new
interactions since the Dalitz plot is sensitive to subtle interference effects.
We also show how transversely polarized $K^*$-mesons give additional
information.
