  Given a connected outerplanar graph G of pathwidth p, we give an algorithm to
add edges to G to get a supergraph of G, which is 2-vertex-connected,
outerplanar and of pathwidth O(p). This settles an open problem raised by
Biedl, in the context of computing minimum height planar straight line drawings
of outerplanar graphs, with their vertices placed on a two dimensional grid. In
conjunction with the result of this paper, the constant factor approximation
algorithm for this problem obtained by Biedl for 2-vertex-connected outerplanar
graphs will work for all outer planar graphs.
