  We consider the problem of stretching pseudolines in a planar straight-line
drawing to straight lines while preserving the straightness and the
combinatorial embedding of the drawing. We answer open questions by Mchedlidze
et al. by showing that not all instances with two pseudolines are stretchable.
On the positive side, for $k\geq 2$ pseudolines intersecting in a single point,
we prove that in case that some edge-pseudoline intersection-patterns are
forbidden, all instances are stretchable. For intersection-free pseudoline
arrangements we show that every aligned graph has an aligned drawing. This
considerably reduces the gap between stretchable and non-stretchable instances.
