  The Wilson coefficient C7 governing the radiative electromagnetic decays of B
meson has been calculated to a very high accuracy in the Standard Model, but
experimental bounds on either the magnitude or the sign of C7 are often
model-dependent. In the present paper, we attempt at constraining both the
magnitude and sign of C7 using a systematic approach. We consider already
measured observables like the branching ratios of B \rightarrow Xs mu+ mu- and
B \rightarrow Xs gamma, the isospin and CP asymmetries in B \rightarrow K*
gamma, as well as AFB and FL in B \rightarrow K*l+l-. We also discuss the
transverse observable AT2 which, once measured, may help to disentangle some of
the scenarios considered. We explore the constraints on C7, C9, C10 as well as
their chirality-flipped counterparts. Within our framework, we find that we
need to extend the constraints up to 1.6 sigma to allow for the "flipped-sign
solution" of C7. The SM solution for C7 exhibits a very mild tension if New
Physics is allowed in dipole operators only. We provide semi-numerical
expressions for all these observables as functions of the relevant Wilson
coefficients at the low scale.
