  A dedicated measurement of additional radiation in
$e^+e^-\to\mu^+\mu^-\gamma$ and $e^+e^-\to\pi^+\pi^-\gamma$
initial-state-radiation events is presented using the full BABAR data sample.
For the first time results are presented at next-to- and
next-to-next-to-leading order, with one and two additional photons,
respectively, for radiation from the initial and final states. Comparison with
predictions from Phokhara and AfkQed Monte Carlo generators is performed,
revealing discrepancies in the one-photon rates and angular distributions for
the former. This disagreement has a negligible effect on the BABAR measurement
of the $e^+e^-\to\pi^+\pi^-(\gamma)$ cross section, but could affect other
measurements significantly. This study sheds a new light on the longstanding
discrepancy in this channel that affects the theoretical prediction of hadronic
vacuum polarization contributions to the muon magnetic moment anomaly.
