Topically applicable, photostable cosmetic/dermatological UV-screening compositions suited for photoprotecting the skin and the hair, comprise (a) at least one UV-screening dibenzoylmethane compound, (b) at least one UV-screening 1,3,5-triazine compound that is photosensitive in the presence of a dibenzoylmethane compound, and (c) a 1,3,5-triazine photostabilizing amount of at least one 4,4-diarylbutadiene compound, formulated into a topically applicable, cosmetically/dermatologically acceptable support therefor; the weight ratio of the 4,4-diarylbutadiene compound(s) to the dibenzoylmethane compound(s) is characteristically greater than 2.5 and the subject compositions are advantageously devoid of any cinnamate sunscreen.