A process for making an alcohol-containing frozen comestible substantiallydevoidof ice crystal agglomerations and/or ice crystal striations and/or trapped airand/or liquidsand products thereof is provided. The process comprises rapidly solidifying analcohol-containing liquid composition so as to produce a substantially single-phase solidalcohol-containing admixture. The single-phase solid alcohol-containingadmixture, and/or piecesthereof, is then tempered by raising the temperature thereof so as to softenthe single-phasesolid alcohol-containing admixture and/or meld the pieces thereof into asingle temperedmass. The single tempered mass is then re-hardened by reducing the temperaturethereof.Also, a process for incorporating the single-phase solid frozen alcohol-containingadmixture into a non-alcohol-containing composition is provided.