  In Dynamic-Frame Aloha subsequent frame lengths must be optimally chosen to
maximize throughput. When the initial population size ${\cal N}$ is known,
numerical evaluations show that the maximum efficiency is achieved by setting
the frame length equal to the backlog size at each subsequent frame; however,
at best of our knowledge, a formal proof of this result is still missing, and
is provided here. As byproduct, we also prove that the asymptotical efficiency
in the optimal case is $e^{-1}$, provide upper and lower bounds for the length
of the entire transmission period and show that its asymptotical behaviour is
$\sim ne-\zeta \ln (n)$, with $\zeta=0.5/\ln(1-e^{-1})$.
