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We discuss the advantages of combining the experimental bound on Br(B_s ->mu+ mu-) and the measured Br(B -> K l+l-) to get the model independentconstraints on physics beyond the Standard Model. Since the two decays givecomplementary information, one can study not only the absolute values of theWilson coefficients that are zero in the Standard Model, but also their phases.To identify the sector in which the new physics might appear, information aboutthe shapes of the transverse asymmetries in B -> K* l+l- at low q^2's can beparticularly useful. We also emphasize the importance of measuring theforward-backward asymmetry in B -> K l+l- decay at large q^2's.

Complementarity of the constraints on New Physics from B_s -> mu+ mu- and from B -> K l+l- decays