France is vehemently opposed to majority voting in cultural matters and trade decisions; Germany will not give up the veto on immigration and asylum; Spain, Portugal and Greece insist on keeping it for regional aid, where they are big beneficiaries.
Comments by European Commission President Romano Prodi that the Nice summit is at risk of failure reflects the big decisions that the European Union needs to take.
The summit has to decide on reforming the way the EU takes decisions, before it is greatly expanded with the admission of new members from central and eastern Europe
Mr Prodi is especially worried about the lack of agreement so far on expanding the number of areas where member states would give up their right of veto over EU decisions.
Already about 80% of decisions by the Council of Ministers are taken by majority vote, but the key issues where unanimity is still required are among the most difficult.
National interests
The UK is often singled out as the objector-in-chief: it insists it will not give up the veto on tax matters or social security, for example. But it is not without allies, and almost all 15 member states have their red lines in one area or another.
France is vehemently opposed to majority voting in cultural matters and trade decisions; Germany will not give up the veto on immigration and asylum; Spain, Portugal and Greece insist on keeping it for regional aid, where they are big beneficiaries.
According to Mr Prodi, the majority voting question is the most important to be settled at the Nice summit, since the retention of the veto, he says, will paralyse an enlarged European Union of 25 or 30 members.
The risk here is not so much that there will be no agreement at all, but that the agreement at Nice might be one that the Commission would regard as totally inadequate.
But another sticking point in the negotiations could prevent any deal being reached in Nice.
That is the big member states' demand for a greater say in decision-making to reflect the size of their populations - what is called re-weighting the votes in the complex system of arriving at a majority in the Council of Ministers.
It is an argument between big and small states, but Germany also thinks it should have more votes than the other big countries because it has more people. France is particularly upset by this.