In A Conformal Energy for Simplicial Surfaces, Alexander Bobenko proves that convex simplicial spheres have vanishing discrete Willmore energy and conjectures that the discrete Willmore minimizers of simplicial spheres of non-inscribable combinatorial types have their energy quantized to integer multiples of 2π. The collection below of discrete Willmore spheres obtained by numerical minimization of the energy supports this conjecture. The examples predominantly have their vertices lying on a sphere so their circumcircles define a non-Delaunay circle pattern on the two-sphere.