From across Ban Jelacic Square in the heart of Zagreb, I saw what looked like folk dancers from rural Croatia performing a post-harvest, pre-drinking polka ritual.
Wherever you go in Croatia, you stand a high chance of being ambushed by folk dancers, so of itself this was not novel.
What drew me over to the platform where they were performing was that it was midday and so hot that I was already cooking in a vat of my own sweat.
The EU demands that Zagreb hand over General Gotovina
"How on earth," I thought, "could these people leap about so enthusiastically in such thick clothing?" I wanted to see if they were frail humans like myself.
But as I approached I was struck by something else. When I heard them more clearly, I realised they were singing in Polish and then I saw a banner announcing them as participants in the annual European Folk Dancing Fair.
Mingling with the tourists and passers-by were dancers and musicians from Slovakia, Italy and Latvia.
Not being a musicologist nor a follower of east and central European folk fashion, I found it hard to differentiate between Cloggies from Poland and Latvia and Cloggies from Croatia.
Well, the truth is I could only think of one thing and it had nothing to do with swirling skirts and celebratory whoops - the Polish and Latvian dancers will become citizens of the European Union next year, the Croats will not.
The present Croatian Government, which has been in power since early 2000, is something of a miracle.
It is a five-party coalition whose members switch partners and swap chairs around the cabinet table so frequently that they might even be eligible for the European Folk Dancing Fair.
The government remains intact for two reasons. First, there are the puppetry skills of the Prime Minister Ivica Racan, a former communist whose ability to play one ambitious party leader off against another is legendary.
The other is the desire of the coalition members, whether opportunistic or genuine is not important here, to shed independent Croatia's association with its founder and first President, Franjo Tudjman.
Fortunately for his ego, Tudjman died before the war crimes tribunal in The Hague could indict him to stand trial next to his nemesis and friend - more friend in my opinion - Serbia's Slobodan Milosevic.
But his legacy remains a troubling burden for the Croatian Government, whose chief foreign and domestic policy is the drive to secure EU membership.
If the European Union were to judge a country's suitability for membership on economic criteria - or indeed folk dancing - then Croatia would at least be level if not ahead of Bulgaria and Romania, who are scheduled to join in 2007.
But the EU does not work like that.
Croatia has other hurdles to leap. Above all it must find and hand over General Ante Gotovina, the Croat equivalent of the notorious Bosnian Serb, Ratko Mladic.
General Gotovina stands accused of the murder and disappearance of hundreds of Serb civilians during the Croat offensive in the Krajina region in 1995.
To many Croats, he is a war hero because of his role in defending the ancient port city of Zadar from attack by Serb militias and the Yugoslav National Army.
Although he is on the run, The Hague and key EU member states, including Britain, are adamant that the government in Zagreb is responsible for his delivery.
If General Gotovina remains in hiding, the EU will not even consider membership for Croatia.
Croatia, however, upped the stakes earlier this year by submitting a formal application to join - cue an extended period of chin-stroking and hesitation in Brussels and the capitals of the member states.
Even if he is handed over, the Croats now wait on tenterhooks until next June to see what the response will be.
All the western Balkan countries are now somewhere in the labyrinthine waiting area of the EU but Croatia's bid has become crucial for all them.
Given Croatia's relative economic health, they argue, if it does not receive a positive signal from the EU, then the rest of us stand no chance at all.
Even Serbia and Bosnia-Hercegovina - those countries that were at war with Croatia or Croat-backed militias - are privately supporting the idea.
So although the issue of Croatia's membership may appear from afar a little obscure, its implications for Europe's most unstable region are immense.
If Croatia is going to trailblaze the Balkans into a new era of prosperity and stability, it will need to shed any hint of the violent nationalism that was visited upon its minority Serbs and the Muslims of Bosnia-Hercegovina a decade ago.
If it wants to be invited to the great European ball, it must learn to dance better than the Poles and the Latvians.