Before revision:  We show that if \mathcal A is stretchable and every edge e either entirely lies on a pseudoline or intersects at most one pseudoline , then G and \mathcal A have a straight-line aligned drawing.
After revision:  We show that if \mathcal A is stretchable and every edge e either entirely lies on a pseudoline or it has at most one pseudoline , then G and \mathcal A have a straight-line aligned drawing.