  We investigate the voting rules in the Council of the European Union. It is
known that the current system, according to the Treaty of Nice, and the voting
system proposed in the Lisbon treaty both strongly deviate from the square root
law by Penrose. This is known to be the ideal voting rule under certain
assumptions. In 2004 Slomczynski and Zyczkowski designed a voting system, now
known as the Jagiellonian Compromise. It satisfies the square root law with
very high accuracy. Each member state in this system obtains a voting weight
proportional to the square root of the population. Additionally the quota is
fixed in such a way that the voting power of each country is also proportional
to the square root of the population.
  In this paper we investigate to which extent a change of the quota in the
Treaty of Nice and the Treaty of Lisbon may bring the voting power closer to
the ideal square root distribution. Our computations show that even with
optimal quota both systems are way off the ideal power distribution.
