  Alon, Seymour and Thomas [1990] proved that every $K_t$-minor-free graph has
a balanced separator of size at most $t^{3/2}n^{1/2}$ vertices. In fact, they
proved a stronger result in terms of `havens'. By the duality of havens and
treewidth they concluded that every $K_t$-minor-free graph on $n$ vertices has
treewidth less than $t^{3/2}n^{1/2}$. This note reproves the latter result
without using havens or any form of treewidth duality. Instead, the proof
directly constructs a tree-decomposition of $G$ with width less than
$t^{3/2}n^{1/2}$.
