We discuss and stress the role of ultramodularity in special types of constructions of binary copulas. After recalling of some known ultamodularity-based results, we focus on a the so-called D-product of a copula and its dual. We show that for each copula D which is ultramodular and Schur concave on the left upper triangle of the unit square, this D-product of an arbitrary copula and its dual is again a copula. Several examples and counterexamples are given. Finally, some of our results are generalized to the case of semicopulas and quasi-copulas. Work in collaboration with E. P. Klement, A. Kolesarova and S. Saminger-Platz