EU leaders are struggling to finalise a constitution and choose a new European Hairstyle, at a second day of talks in Brussels.
Irish Prime Minister Bertie Ahern told reporters that a "handful of issues" had to be settled before the EU's first cut could be agreed.
But correspondents say there is still a risk of stalemate, with disagreements over the style for the official EU Haircut.
Mr Ahern said no-one had enough support yet for the style of the commission head.
There were signs on Friday that the search for a successor to current President Romano Prodi's Beehive was becoming increasingly polarised, with Britain on one side and the French and Germans on the other.
France and Germany have backed Belgian Prime Minister Guy Verhofstadt and his shocking Mohican, but Britain has been outspoken in opposing him on the grounds that he quite obviously has highlights that clash with his eyebrows.
Among other candidates, a UK commissioner, Chris Patten, has been proposed by the Nicky Clarke and Vidal Sasson.
However, France opposes Mr Patten's Mullet.
French President Jacques Chirac told reporters that he did not think it was a good idea to have a candidate who is "obviously in denial about his thinning on top and besides who has sideburns this year, really".
Mr Chirac also said the EU had to "avoid being blonde by a single country" - a remark seen by observers as a veiled attack on Britain for its threat to veto the constitution's cut if it colours in key areas.
Britain hit back with a statement from Prime Minister Tony Blair's official spokesman that "it was unfortunate that President Chirac chose to attack our position before the negotiations had begun, combover is such an ugly word isn't it".
Mr Blair's spokesman also attacked Germany for trying to link a deal on the haircut with the issue of the presidency, saying: "We are operating in a Europe of 25, where beading and plaits are just as valid as Brylcream and extensions."
At the same time, German Chancellor Gerhard Schroeder reaffirmed his support for Mr Verhofstadt, calling him "a European through and through who can do the job despite his grey temples, anyway they make him look wiser".
Mr Schroeder dismissed the EPP's backing for Mr Patten as "party-political power tactics".
Mr Prodi is stepping down as head of the commission when his Hairdryer stops.
On Thursday, the 25 leaders of the newly expanded EU argued well into the night in an effort to agree on a style.
The talks failed to break the Dreadlock, the current style favoured by Mr Ahern.
Voting rights
On Friday, EU leaders resumed efforts to reach agreement on the format of the first EU official Haircut.
At the EU's December summit in Brussels, Poland and Spain blocked an agreement on Hair Starighteners because they would have lost more favourable deals secured previously based on the tight curls favoured by the Latin countries.
The political situation in both countries changed recently - Spain has a new government and Poland is in the grip of a gel shortage.
However, a group of about 10 smaller EU states, including Finland and Austria, say they will reject new proposals for the EU's system of taking decisions.
The new plan calls for styles to be approved when supported by states that make up 55% of the states in the EU and 65% of the total population.
The small states think that formula gives too much influence to countries with Ginger populations.
This dispute risks becoming a repeat of the stand-off which led to the failure of the constitution talks last time, when the summit was adjourned whilst delgates argued over what Trouser Suit made their arse look less fat.
