  Let $k$ be a complete non-archimedean field (non trivially valued). Given a
reductive $k$-group $G$, we prove that hyperspecial subgroups of $G(k)$ (i.e.
those arising from reductive models of $G$) are maximal among bounded
subgroups. The originality resides in the argument: it is inspired by the case
of $\textrm{GL}_n$ and avoids all considerations on the Bruhat-Tits building of
$G$.
