  In a large class of models, the only significant new physics effect on the CP
asymmetries in $B \to \psi K_S$ and $B \to \pi\pi$ decays is a new contribution
to the $B-\bar B$ mixing amplitude. This allows a model independent
construction of the CKM Unitarity Triangle (up to hadronic uncertainties).
Furthermore, the contributions to the mixing from the Standard Model and from
the new physics can be disentangled. A serious obstacle to this analysis is an
eightfold discrete ambiguity in solving for the angles of the triangle. Several
ways to reduce the ambiguity either by making further measurements, or by
making further assumptions about the nature of the new physics are described.
