  We present a general purpose, parton-level Monte Carlo program for the
calculation of the radiative ($L\to\nu\bar\nu l+\gamma$) and rare
($L\to\nu\bar\nu l'+ l^+l^-$) muon and tau decays at NLO in the effective Fermi
theory. In the case of muon, these processes are irreducible Standard Model
backgrounds to searches for lepton flavour violation at the PSI experiments MEG
and Mu3e as they become indistinguishable from the corresponding signals when
the neutrinos carry little energy.
  Furthermore, we argue that fully differential NLO corrections are very
important for the analysis of measurements aiming at the percent level or
better. This is especally true if very stringent phase-space cuts are applied.
To illustrate this, we use a tension between BaBar's recent measurement of the
radiative tau decay and the Standard Model prediction as an example of such an
analysis. Finally, we present the branching ratios of the rare tau decay
$\tau\to\nu\bar\nu l' l^+l^-$ at NLO.
  We generally find that QED corrections of $\mathcal{O}(10\%)$ are very well
possible.
