  Using the automation program GoSam, fully differential NLO corrections were
obtained for the rare decay of the muon $\mu\to e\nu\bar\nu ee$. This process
is an important Standard Model background to searches of the Mu3e collaboration
for lepton-flavour violation, as it becomes indistinguishable from the signal
$\mu\to 3e$ if the neutrinos carry little energy. With our NLO program we are
able to compute the branching ratio as well as custom-tailored observables for
the experiment. With minor modifications, related decays of the tau can also be
computed.
