It is proved that if, from the minimal corepresentation of a pro-p-group ~ of cohomology dimension two with a free commutant, a part of the relations is discarded, then one obtains a minimal corepresentation of a pro-p-group, the cohomology dimension of which is equal to two and the commutant of which is free. For such pro-pgroups, F(~) < ~(~) , where ~) is the minimal number of generators of the finitely generated pro-p-group ~ and ~ [~) is the minimal number of relations.Conversely, if ~ is a finitely generated pro-p-group of cohomology dimension two with a free conmmtant, then, for it, any minimal system of relations can be complemented to give a system of relations such that the pro-p-group ~/ thus obtained has c0homology dimension two, its commutant is free, and, moreover, ~(~I)= ~(~t)-1 =~G) -~