Simply slicing knots

Given a simply-connected 4-manifold X with boundary S^3, when is a knot K sliced by a simple disc in X, i.e. when does K bound a disc in X whose complement has abelian fundamental group? When X is the 4-ball, Freedman proved that this occurs if and only if the knot has Alexander polynomial one. This talk is concerned with the above question in more general 4-manifolds and is based on joint projects with Orson, Pencovitch, Piccirillo and Powell.