  In this paper we classify branched Willmore spheres with at most three branch
points (including multiplicity), showing that they may be obtained from
complete minimal surfaces in $\R ^ 3$ with ends of multiplicity at most three.
This extends the classification result of Bryant. We then show that this may be
applied to the analysis of singularities of the Willmore flow of non-Willmore
spheres with Willmore energy $ \mc {W} (f) \leq 16\pi$.
