The construction of group ring elements that annihilate the ideal class groups of totally complex abelian extensions of ℚ is classical and goes back to work of Kummer and Stickelberger. A generalization to totally complex abelian extensions of totally real number fields was formulated by Brumer. Brumer’s formulation fits into a more general framework known as the Brumer-Stark conjecture. We will verify this conjecture for a large number of examples belonging to an extended class of situations where the general status of the conjecture is still unknown.