  Use of semi-leptonic decays has become standard in constraining the Unitarity
Triangle. Bearing in mind that precise calculations of these are very
challenging, we propose an entirely new approach. In particular the |Vcb| +
epsilon_K constraint, which depends extremely sensitively on Vcb in the
traditional method, is replaced by the interplay between epsilon_K, BR(B ->tau
nu) and Delta M_Bs. It is found that even in this method tensions with the
Standard Model persist at the ~1.8 sigma level. Furthermore, improvements on
the B -> tau nu branching ratio and on the lattice determination of f_Bs
Bs^(1/2) can increase the effectiveness of this method significantly.
