A process for making an alcohol-containing frozen comestible substantially devoid of ice crystal agglomerations and/or ice crystal striations and/or trapped air and/or liquids and products thereof is provided. The process comprises rapidly solidifying an alcohol-containing liquid composition so as to produce a substantially single-phase solid alcohol-containing admixture. The single-phase solid alcohol-containing admixture, and/or pieces thereof, is then tempered by raising the temperature thereof so as to soften the single-phase solid alcohol-containing admixture and/or meld the pieces thereof into a single tempered mass. The single tempered mass is then re-hardened by reducing the temperature thereof. Also, a process for incorporating the single-phase solid frozen alcohol-containing admixture into a non-alcohol-containing composition is provided.