The dispute over EU voting weights pits Germany - the biggest EU state - against Poland the biggest of the 10 new members joining the union in May.
Stubborn?: The Polish and Spanish foreign ministers
The problem arose because the EU believes big states deserve greater voting power than small ones.
In other words, Germany, with a population of 82.5 million, gets to wield more power in the EU Council of Ministers than Luxembourg, with its population of 453,000.
So as part of the EU's preparations for the forthcoming enlargement, it agreed on a new allocation of voting weights - for old and new members - at a summit Nice in December 2000.
The biggest winners were Poland and Spain, who came away with 27 votes, only two less than the big four - France, Germany, Italy and the UK.
This was despite the fact that their populations (38.6 million and 41 million respectively) are much smaller.
The system agreed at Nice was very complicated.
The new EU draft constitution suggests, instead, a very simple system.
It says a vote is passed when it has the support of 50% of countries, representing 60% of the EU's population.
Poland and Spain automatically lose everything they gained at Nice.
Spain already had a reputation as a stubborn negotiator (rather like the UK) before Poland came along. United on this issue, and on some others, they are regarded as the new "awkward squad".
However, both countries deny that they are resisting the voting system proposed in the draft constitution purely out of self-interest.
Poland has argued that the system gives the big countries too much weight, and says it is acting on behalf of all the EU's smaller countries.
As by far the largest of the mainly small 10 new member states, it is setting itself up as a leader of the new boys - and may be recognised as such by some of them.
Germany, meanwhile, indicated it would answer stubbornness with stubbornness.
As the biggest net creditor to the EU budget, Berlin has threatened to turn off the flow of cash to Spain, which is a big recipient of EU funds, and to Poland, which will be one of the biggest recipients for years to come.
How can a compromise be reached?
One possibility would be to modify the system proposed in the constitution - so that a vote would be passed with the support of 50% of member states comprising 50% of the population, or 60% of member states comprising 60% of the population.
Another possibility would be to delay the implementation of the new system for 10 years or more, allowing Spain and Poland a chance to influence key decisions on the future EU budget under the Nice system.
Other forms of bargaining are also possible. Carrots theoretically available to be held out include
extra seats in the European parliament and promises of cash for regional aid.
A decision on the constitution must be made unanimously and then needs to be ratified in each member state - either by parliament, or in a public referendum.