  We consider a branching-selection particle system on the real line. In this
model the total size of the population at time $n$ is limited by $\exp\left(a
n^{1/3}\right)$. At each step $n$, every individual dies while reproducing
independently, making children around their current position according to
i.i.d. point processes. Only the $\exp\left(a(n+1)^{1/3}\right)$ rightmost
children survive to form the $(n+1)^\mathrm{th}$ generation. This process can
be seen as a generalisation of the branching random walk with selection of the
$N$ rightmost individuals, introduced by Brunet and Derrida. We obtain the
asymptotic behaviour of position of the extremal particles alive at time $n$ by
coupling this process with a branching random walk with a killing boundary.
