  In SODA'99, Chan introduced a simple type of planar straight-line upward
order-preserving drawings of binary trees, known as LR drawings: such a drawing
is obtained by picking a root-to-leaf path, drawing the path as a straight
line, and recursively drawing the subtrees along the paths. Chan proved that
any binary tree with $n$ nodes admits an LR drawing with $O(n^{0.48})$ width.
In SODA'17, Frati, Patrignani, and Roselli proved that there exist families of
$n$-node binary trees for which any LR drawing has $\Omega(n^{0.418})$ width.
In this note, we improve Chan's upper bound to $O(n^{0.437})$ and Frati et
al.'s lower bound to $\Omega(n^{0.429})$.
