Many prior art processes for cleaning predominantly organic hard surfaces have been found to be considerably less effective in removing very fine particles on such surfaces than are the best cleaners for metallic surfaces. However, it has been found, and forms the basis of this invention, that fine particles can be removed effectively from organic surfaces by an indirect process of first forming a thin solid coating over the surface and then removing the solid coating, into which the fine particles that formerly contaminated the surface to be cleaned have presumably become incorporated. Substantially hydrolyzed poly(vinyl acetate) has been found particularly useful for forming the thin solid coating when this coating is to be removed by treatment with an acidic aqueous solution; acrylate polymers are preferred if the solid coating is to be removed by an alkaline aqueous solution. In either instance, in order to obtain good wetting without damaging the surface to be cleaned, the material that forms the bulk of the solid coating is preferably applied to the surface to be cleaned in an aqueous solution or dispersion that also contains surfactant molecules that include imidazoline moieties. A method of quantifying the degree of removal of solid particles is also provided.