  We initiate the study of the following problem: Given a non-planar graph G
and a planar subgraph S of G, does there exist a straight-line drawing {\Gamma}
of G in the plane such that the edges of S are not crossed in {\Gamma} by any
edge of G? We give positive and negative results for different kinds of
connected spanning subgraphs S of G. Moreover, in order to enlarge the subset
of instances that admit a solution, we consider the possibility of bending the
edges of G not in S; in this setting we discuss different trade-offs between
the number of bends and the required drawing area.
