  A semi--numerical approach proposed many years ago for describing
gravitational collapse in the post--quasi--static approximation, is modified in
order to avoid the numerical integration of the basic differential equations
the approach is based upon. For doing that we have to impose some restrictions
on the fluid distribution. More specifically, we shall assume the vanishing
complexity factor condition, which allows for analytical integration of the
pertinent differential equations and leads to physically interesting models.
Instead, we show that neither the homologous nor the quasi--homologous
evolution are acceptable since they lead to geodesic fluids, which are
unsuitable for being described in the post--quasi--static approximation. Also,
we prove that, within this approximation, adiabatic evolution also leads to
geodesic fluids and therefore we shall consider exclusively dissipative
systems. Besides the vanishing complexity factor condition, additional
information is required for a full description of models. We shall propose
different strategies for obtaining such an information, which are based on
observables quantities (e.g. luminosity and redshift), and/or heuristic
mathematical ansatz. To illustrate the method, we present two models. One model
is inspired in the well known Schwarzschild interior solution, and another one
is inspired in Tolman VI solution.
