One of the useful consequences of the geometrisation of 3-manifolds is that it leads to control over embedded surfaces. If one makes an essential surface minimal within a hyperbolic 3-manifold, the surface then inherits a negatively curved metric, and this has geometric and topological applications. In my talk, I will explain how in the case of knot complements, one can arrange for embedded essential surfaces to inherit a non-positively curved metric, even when no hyperbolic metric on the knot complement is given. This has some striking consequences, particularly for the knot classification problem.