  We study the upward point-set embeddability of digraphs on one-sided convex
point sets with at most 1 bend per edge. We provide an algorithm to compute a
1-bend upward point-set embedding of outerplanar $st$-digraphs on arbitrary
one-sided convex point sets. We complement this result by proving that for
every $n \geq 18$ there exists a $2$-outerplanar $st$-digraph $G$ with $n$
vertices and a one-sided convex point set $S$ so that $G$ does not admit a
1-bend upward point-set embedding on $S$.
