  We consider straight-line outerplanar drawings of outerplanar graphs in which
a small number of distinct edge slopes are used, that is, the segments
representing edges are parallel to a small number of directions. We prove that
$\Delta-1$ edge slopes suffice for every outerplanar graph with maximum degree
$\Delta\ge 4$. This improves on the previous bound of $O(\Delta^5)$, which was
shown for planar partial 3-trees, a superclass of outerplanar graphs. The bound
is tight: for every $\Delta\ge 4$ there is an outerplanar graph with maximum
degree $\Delta$ that requires at least $\Delta-1$ distinct edge slopes in an
outerplanar straight-line drawing.
