I will describe ongoing joint work with Johan Martens about moduli spaces of principal bundles, with reductive structure
group, on a twice-punctured curve of genus zero.  I will explain how they can be used to construct the wonderful
compactification of the group in the sense of De Concini-Procesi if the group has trivial center.  Furthermore, if the
group has nontrivial center, we get a new compactification which is a smooth Deligne-Mumford stack.