The conditional distributivity, that is distributivity equation with additional restriction imposed on the domain of aggregation operations, is an issue of interest for many different theoretical and practical areas, special for integration theory and utility theory. This paper presents new results on this specific form of distributivity for semi-t-operators over conjunctive uninorms. Since the observed class of uninorms is rather wide and includes not only the continuous case, the presented research is an extension of some well-known results and provides wider classes of solutions.