  We revise the radiative corrections to double-Dalitz decays
($P\to\ell\bar{\ell}\ell'\bar{\ell}'$), completing the full next-to-leading
order calculation in QED as compared to existing calculations. As a result, we
find mild differences with respect to previous studies, that might be relevant
for extracting information about the mesons transition form factors. The latter
play an important role in determining the hadronic light-by-light contribution
to the anomalous magnetic moment of the muon. Finally, we outline an ongoing
extension of this work to the $e^+e^-\to e^+e^- P$ processes.
