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 with $L\in\{\tau,\mu\}$ and $l,l'\in\{\mu,e\}$. 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 \textsc{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.