I will explain what the Willmore Morse Index of unbranched Willmore spheres in Euclidean three-space is and how to compute it. These Willmore spheres are inverted minimal surfaces with embedded planar ends. It turns out that the number of logarithmically growing Jacobi fields on the minimal surface are very important for the computation of the Willmore Morse Index. One consequence of our analysis is that all unbranched Willmore spheres are unstable (except for the round sphere). This talk is based on work with Jonas Hirsch.