  Based on explicitly gauge invariant interpolating operators we compute
complete next-leading order QED-corrections for leptonic decays. These are
sizeable since the helicity-suppression in V-A interactions allows for
structure-dependent collinear logs. We have explicitly checked that these logs
are absent for helicity-unsuppressed Yukawa-type transitions. Based on $B \to
\gamma$ form factors we present the rates for $B^- \to (\mu^-,\tau^-) \bar \nu
(\gamma)$ in differential and integrated form as a function of the photon
energy cut-off $E_\gamma^{\text{cut}}$. The effect of the virtual
structure-dependent corrections are approximately $+5\%$ and $+3\%$ for the
$\mu$- and $\tau$-channel respectively. The structure dependence of the real
radiation exceeds that of the virtual one for $E_\gamma^{\text{cut}}|_{\mu} >
0.18(3)$ GeV and is subdominant for the tau channel even when fully inclusive.
