The LHCb experiment has made several measurements in b→s transitions which indicate tensions with the Standard Model predictions. Assuming the source of these tensions to be new physics, we present new global fits to all Wilson coefficients which can effectively receive beyond the Standard Model contributions. While the theoretically clean ratios RK(⁎) which are sensitive to lepton flavour non-universality may unambiguously establish lepton non-universal new physics in the near future, most of the other tensions with the SM in the b→s data, in particular in the angular observables of the B→K⁎μμ decays and in the branching ratios of the Bs→ϕμμ decays, depend on the estimates of non-factorisable power corrections. Therefore, we also analyze the dependence of the new global fit on these corrections.