  The phenomenology from the time of the quench to the asymptotic behavior in
the phase-ordering kinetics of a system with conserved order parameter is
investigated in the Bray-Humayun model and in the Cahn-Hilliard-Cook model.
  From the comparison of the structure factor in the two models the generic
pattern of the overall time evolution, based on the sequence ``early linear -
intermediate mean field - late asymptotic regime'' is extracted. It is found
that the time duration of each of these regimes is strongly dependent on the
wave vector and on the parameters of the quench, such as the amplitude of the
initial fluctuations and the final equilibrium temperature. The rich and
complex crossover phenomenology arising as these parameters are varied can be
accounted for in a simple way through the structure of the solution of the
Bray-Humayun model.
