The 2 Higgs Doublet Model of type III has renormalisable Lepton Flavour-Violating couplings, and its oneand two-loop ("Barr-Zee") contributions to μ → eγ are known. In the decoupling limit, where the mass scale M of the second doublet is much greater than the electroweak scale, the model can be parametrised with an Effective Field Theory (EFT) containing dimension-six operators. The 1/M 2 terms of the exact calculation are reproduced in the EFT, provided that the four-fermion operator basis below the weak scale is enlarged with respect to the SU(2)-invariant BuchmullerWyler list. It is found that the dominant two-loop "Barr-Zee" contributions arise mostly in two-loop matching and running, and that dimension-eight operators might be numerically relevant.