The a priori voting powers of member countries in the council of ministers of the European Union have been discussed in the literature mainly from the view-point of Banzhaf and Shapley-Shubik indices. This paper discusses - in the light of these and other more recent (Colomer's, Holler's as well as Deegan and Packel's) power indices - the interaction of the council ministers and the European Parliament (EP) under the assumption that the consent of both bodies is needed to carry a motion or piece of union-wide legislation. Moreover, the double-majority principle is discussed from the view-point of voting power distribution. Finally we consider the voting power distribution in a three-chamber system consisting of Commission, Council and EP.