  In this Letter we investigate the role of recombination energy during a
common envelope event. We confirm that taking this energy into account helps to
avoid the formation of the circumbinary envelope commonly found in previous
studies. For the first time, we can model a complete common envelope event,
with a clean compact double white dwarf binary system formed at the end. The
resulting binary orbit is almost perfectly circular. In addition to considering
recombination energy, we also show that between 1/4 and 1/2 of the released
orbital energy is taken away by the ejected material. We apply this new method
to the case of the double-white dwarf system WD 1101+364, and we find that the
progenitor system at the start of the common envelope event consisted of a
$\sim1.5M_\odot$ red giant star in a $\sim 30$ day orbit with a white dwarf
companion.
