  Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that
for every planar graph $G$ there is a graph $H$ with treewidth at most 8 and a
path $P$ such that $G\subseteq H\boxtimes P$. We improve this result by
replacing "treewidth at most 8" by "simple treewidth at most 6".
