  Let p be an odd prime and S a finite set of primes = 1 mod p. We give an
effective criterion for determining when the Galois group G=G_S(p) of the
maximal p-extension of Q unramified outside of S is mild when |S|=4 and the cup
product H^1(G,Z/pZ) \otimes H^1(G,Z/pZ) --> H^2(G,Z/pZ) is surjective.
