We study deformations of the SM via higher dimensional operators. In particular, we explicitly calculate the one-loop anomalous dimension matrix for 13 bosonic dimension-6 operators relevant for electroweak and Higgs physics. These scaling equations allow us to derive RG-induced bounds, stronger than the direct constraints, on a universal shift of the Higgs couplings and some anomalous triple gauge couplings by assuming no tuning at the scale of new physics, i.e. by requiring that their individual contributions to the running of other severely constrained observables, like the electroweak oblique parameters or Γ(h → γγ), do not exceed their experimental direct bounds. We also study operators involving the Higgs and gluon fields.