The definition of a pseudo-distributive law of one pseudomonad over another is given in [Theory Appl. Categ. 5, 91–147 (1999; Zbl 0919.18004)] where F. Marmolejo find there the four familiar diagrams given in the original definition of distributive law by J. Beck [Lect. Notes Math. 80, 119–140 (1969; Zbl 0186.02902)], but commutativity is replaced by invertible 2-cells. So, he find nine coherence conditions and a justification of why they should suffice. In the thesis of M. Tanaka (2005) it is suggested that the nine coherence axioms given in that paper are incomplete, in the sense that one of the coherence axioms is missing, a concern echoed by M. Tanaka and J. Power [J. Log. Comput. 16, 5–25 (2006; Zbl 1105.03072)], now in the form one axiom may be missing. It is the authors’ contention that Marmolejo (loc. cit.) is fundamentally correct, if a little corrective in its efforts to provide a complete set of axioms is done. For here in this paper the authors show that in fact eight of the nine axioms of Marmolejo (loc. cit.) suffice.