  Upcoming searches for lepton flavour change (LFV) aim to probe New
Physics(NP) scales up to $ \sim 10^4$ TeV, implying that they will be sensitive
to NP at lower scales that is suppressed by loops or small couplings. We
suppose that the NP responsable for LFV is beyond the reach of the LHC and can
be parametrised in Effective Field Theory, introduce a small power-counting
parameter \`a la Cabibbo-Wolfenstein, and assess whether the existing dimension
six operator basis and one-loop RGEs provide a good approximation for LFV. We
find that mu to e flavour-changing observables can be sensitive to a few dozen
dimension eight operators, and to some effects of two-loop anomalous
dimensions, for NP scales below 20-100 TeV. We also explore the effect of some
simplifying assumptions in the one-loop RGEs, such as neglecting
flavour-changing effects.
