  Three-body recombination in quantum gases is traditionally associated with
heating, but it was recently found that it can also cool the gas. We show that
in a partially condensed three-dimensional homogeneous Bose gas three-body loss
could even purify the sample, that is, reduce the entropy per particle and
increase the condensed fraction $\eta$. We predict that the evolution of $\eta$
under continuous three-body loss can, depending on small changes in the initial
conditions, exhibit two qualitatively different behaviours - if it is initially
above a certain critical value, $\eta$ increases further, whereas clouds with
lower initial $\eta$ evolve towards a thermal gas. These dynamical effects
should be observable under realistic experimental conditions.
