We investigate new-physics contributions to b → s transitions in the context of an effective field theory extension of the Standard Model, including operator mixing at one loop. We identify the few scenarios where a single Wilson coefficient, C/Λ 2 ∼ 1/TeV 2 , induces a substantial shift in the lepton flavour universality ratios RK and RK * at one loop, while evading Z-pole precision tests, collider bounds, and other flavour constraints. Good fits to the present data are achieved by a left-handed current operator with quark-flavour indices (2, 2) or (3, 3), hitherto overlooked. Interestingly, the running of the Standard Model Yukawa matrices gives the dominant effect for these scenarios. We match the favoured effective-theory scenarios to minimal, single-mediator models, which are subject to additional stringent constraints. Notably, we recognise three viable instances of a leptoquark with one coupling to fermions only. If the anomalies were confirmed, it appears that one-loop explanations have good prospects of being directly tested at the LHC.