To combat these problems, the first line of defense has been to polish ever finer curves into the mirror's surface.  This makes smaller hills and shallower valleys.  Here we note that the closer the mirror is polished to perfection, the less it can be distorted at the microscopic level.  Polishing a mirror so that it will just meet Rayleighs Criterion is a sin that will leave the final product prone to microscopic distortions because the hills and valleys of a "diffraction limited" mirror are quite large.
The force producing the sag has both an "Outward component" and a "Downward component".  The traditional way to eliminate sagging has been to make the mirror much thicker with respect to its sagitta.  This produces a "Resultant force" that is much closer to the Outward component, - thereby reducing the effectiveness of the Downward component producing the sag. It is a solution that works very well for small aperture telescopes.  For large aperture telescopes, the extra thickness needed quickly increases the weight of the mirror to unsupportable proportions.
As more and more Astronomers desired larger aperture telescopes, a need developed for combatting sag in a different manner.   Floatation Cells became the answer. They support a thin, large aperture mirror at multiple points, controlling the sag at various radii across the mirror's surface.  Here we see that a thick, small aperture mirror, with a very small wavefront error would not benefit at all from any kind of floatation cell.
Professor David Lewis' "Plop" program is based on "Plate Theory", which only applies to mirrors where the thickness of the mirror is no more than 20% of the mirror's diameter.  Thicker mirrors don't need the assistance of floatation cells to keep their figure.