Translating results due to J. Labute into group cohomological language, A. Schmidt proved that a finitely presented pro-p-group G is mild and hence of cohomological dimension cd G=2 if $H^1(G,F_p)=Uoplus V$ as $F_p$-vector space and the cup-product $H^1(G,F_p)otimes H^1(G,F_p)to H^2(G,F_p)$ maps $Uotimes V$ surjectively onto $H^2(G,F_p)$ and is identically zero on $Votimes V$. This has led to important results in the study of p-extensions of number fields with restricted ramification, in particular in the case of tame ramification. In this paper, we extend Labute's theory of mild pro-p-groups with respect to weighted Zassenhaus filtrations and prove a generalization of the above result for higher Massey products which allows to construct mild pro-p-groups with defining relations of arbitrary degree. We apply these results for one-relator pro-p-groups and obtain some new evidence of an open question due to Serre.