Given a graph G and a subset F ⊆ E(G) of its edges, is there a drawing ofG in which all edges of F are free of crossings? We show that this question can be solved in polynomial time using a Hanani-Tutte style approach. If we require the drawing of G to be straight-line, and allow at most one crossing along each edge in F , the problem turns out to be as hard as the existential theory of the real numbers.