  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 $H^1(G,\F_p)=U\oplus V$ 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
$U\otimes V$ surjectively onto $H^2(G,\F_p)$ and is identically zero on
$V\otimes V$. 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.
