  In a major extension of our previous model (C.W. Gardiner, P. Zoller,
  R.J. Ballagh and M.J. Davis, Phys. Rev. Lett. 79, 1793 (1997)) of condensate
growth, we take account of the evolution of the occupations of lower trap
levels, and of the full Bose-Einstein formula for the occupations of higher
trap levels. We find good agreement with experiment, especially at higher
temperatures. We also confirm the picture of the ``kinetic'' region of
evolution, introduced by Kagan et al, for the time up to the initiation of the
condensate. The behavior after initiation essentially follows our original
growth equation, but with a substantially increased rate coefficient W^{+}.
