In this talk we study the relation between two geometric quantities for smooth closed 2d-surfaces ? ? the Willmore bending energy W (?) and the minimal length of a closed geodesic ?(?). It turns out that for surfaces of Willmore energy less than 6? (with normalized area), ?(?) is bounded below in terms of W (?). The threshold of 6? is optimal for such a result ? we will see that surfaces above this threshold can indeed have geodesic bottlenecks. Our inequality can be proved very easily if one assumes that the shortest closed geodesic has no self-intersections. The discussion of this assumption leads to intriguing insights. This is joint work with Fabian Rupp (Vienna) and Christian Scharrer (Bonn).