This means they are now free to concentrate on the two chapters remaining on the table, agriculture and budget, when the EU provides them with its own negotiating position, probably by early November.
But the real story appears to be the relatively strong performances of the three Baltic countries and Slovakia. Latvia and Slovakia are just one chapter behind the four leaders. Both, along with Lithuania, were originally relegated to a "second wave" of accession hopefuls, behind expected front-runners like Hungary, Poland, and the Czech Republic.
The success of Latvia, Lithuania, and Slovakia confirms what EU leaders made obvious last December when they named the 10 candidate countries that can hope to join the bloc in 2004. The former second wave was then officially split into two parts: Latvia, Lithuania, Slovakia, and Malta gained a firm foothold in the first wave, along with Poland, Hungary, the Czech Republic, Slovenia, Estonia, and Cyprus; Bulgaria and Rumania must now wait until 2007.
Michael Emerson, an analyst with the Brussels-based Centre for European Policy Studies, said the concept of "waves" in the enlargement process underwent a radical shift months ago.
"The next accession candidates (are) the new 'first wave' - for me that's the 10. The 'second wave' then would be Bulgaria and Rumania. The 'third wave' may be Croatia, may be Turkey, and so forth," Emerson said.
Emerson said the present first wave expecting to join the EU in 2004 had become what he called a "fairly homogeneous group" facing essentially similar challenges. He said the catch-up of Latvia, Lithuania and Slovakia with the original front-runners has come at no particular cost with respect to these countries' long-term interests.
"Speaking of long-term interests, absolutely not; short-term discomfort is a question, but broadly speaking, I think the evidence is that when you're approaching joining the European Union as a full member state, you might as well get it over with as fast as possible," Emerson said.
When EU leaders decided in December 1999 to open accession talks with an additional six countries, first-wave governments that had started negotiations two years earlier feared this would slow down their progress. In retrospect, there is no indication that has happened.
The main factor here seems to have been that while first-wave countries had to wait for the EU member states to come up with negotiating positions on each chapter, second-wave countries faced no such obstacle and were able to clinch deals quickly that do not differ substantively from those achieved by the first wave.
Politicians in some first-wave countries have also expressed fears that the EU might be turning a blind eye to the second wave's questionable ability actually to implement EU laws.
Emerson said he did not think that the EU has given any special treatment to Latvia, Lithuania, or Slovakia. He said that only political factors, such as the possible election in Slovakia this year of former nationalist Prime Minister Vladimir Meciar, could impede a country's progress.
"I wouldn't know how to really differentiate among these 10 countries. There are some political factors, highly political factors, but that's a different question, rather than administrative capacity....If, in forthcoming elections, Mr. Meciar is elected prime minister of Slovakia, there's a problem," Emerson said.
In fact, the most obvious dividing line between the 10 leading candidates cuts across any "wave" distinctions. That is because the Czech Republic, Hungary, Malta, Poland, and Slovakia have so far been unable to close talks on the competition chapter. The four Central European countries share the same post-communist industrial heritage that now needs to be propped up by substantial state aid, which runs counter to EU competition-policy rules.
The final question is whether the inclusion of a second wave in accession talks in December 1999 could have had an impact on the timing of enlargement as a whole.
Again, Emerson does not think the second wave has made a detectable difference. He said the dynamics of the process had been largely determined by the progress of Poland, the biggest country seeking admission to the EU.
"I don't actually think it's made much difference. If you look at the problems with Poland - the biggest candidate and with considerable problems - you wouldn't really say that the Polish questions have been affected (by the inclusion of the second wave)," Emerson said.
"Nature has taken its course," he said, and neither the advancement of negotiations nor their expected closure in Copenhagen in December has been slowed down.