In a major extension of our previous model [Phys. Rev. Lett. 79, 1793 (1997
)] of condensate growth, we take account of the evolution of the occupation
s of lower trap levels, and of the full Bose-Einstein formula for the occup
ations of higher trap levels. We find good agreement with experiment, espec
ially 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 ini
tiation of the condensate. The behavior after initiation essentially follow
s our original growth equation, but with a substantially increased rate coe
fficient W+.