Let L/K be a �nite Galois CM-extension of number �elds with Galois group G.
In an earlier paper, the author has de�ned a module SKu(L/K) over the center of
the group ring ZG which coincides with the Sinnott-Kurihara ideal if G is abelian
and, in particular, contains many Stickelberger elements. It was shown that a certain
conjecture on the integrality of SKu(L/K) implies the minus part of the equivariant
Tamagawa number conjecture at an odd prime p for an in�nite class of (non-abelian)
Galois CM-extensions of number �elds which are at most tamely rami�ed above p,
provided that Iwasawa's μ-invariant vanishes. Here, we prove a relevant part of this
integrality conjecture which enables us to deduce the equivariant Tamagawa number
conjecture from the vanishing of μ for the same class of extensions.