The treaty changes the distribution of votes on the Council of Ministers, writes Denis Staunton, European Correspondent.
The Council of Ministers is the most powerful body in the EU. It is composed of national government ministers and must approve any new EU measures proposed by the Commission.
Its make-up changes according to the topic under discussion; agriculture ministers deal with farming issues, transport ministers with transport policy etc.
Each member-state is allocated a voting weight which reflects to some extent its population.
At present, Ireland has three votes, while the biggest four countries, Germany, France, Italy and Britain, have 10 each.
In practice, most decisions are worked out in advance by ambassadors meeting in the Council of Permanent Representatives (Coreper).
If a vote is taken among ministers, the outcome is determined by a simple majority, a qualified majority or unanimity, depending on the policy under discussion.
At present, a qualified majority is 62 votes out of a possible 87. However, a blocking minority of 26 votes can defeat any measure.
The Nice Treaty changes the distribution of votes among the member-states. Put simply, smaller states double their present number of votes while the biggest countries triple theirs.
Under the new system, Ireland will have seven votes and Germany 29.
Other changes include a requirement that decisions be approved by a majority of member-states and a "demographic safety-net" where a majority must represent at least 62 per cent of the EU's total population.
The treaty's critics complain that the reweighting of votes will diminish the influence of small countries in the Council of Ministers. At present, Ireland has 2.2 per cent of the votes in the council; under the new system that share would fall to 2 per cent.
The treaty's champions point out that, if the voting system remained unchanged after enlargement, measures could be adopted with the support of less than 50 per cent of the EU's population. They argue that giving more weight to bigger countries is necessary if the EU is to remain democratic.
Some analysts believe that the new voting system will make it more difficult to reach decisions in the Council of Ministers because a qualified majority will now require 74 per cent of the votes and the support countries representing almost two-thirds of the EU's population.