Secondary aggregates are prepared from inert waste fines, from, for example, quarrying and combustion processes, using a combination of accelerated carbonation and tumbling, such that aggregate particles composed of successive layers of solid carbonate-based reaction products form a hard aggregate suitable for use in concrete. The process may carried out by loading the starting materials, and if necessary, water into a cylindrical drum that is rotatable about its horizontal axis, and the interior is charged with a carbon dioxide atmosphere, or mounted within a larger vessel that holds a carbon dioxide atmosphere. Aggregates are formed as coatings on core particles as tumbling proceeds, and the coatings are hardened by in situ formation of carbonates by reaction with the carbon dioxide.