Nowadays, in important ways, this is quite a lot. The Turks are happy to see that the Greek Prime Minister, Costas Simitis, having got the better of anti-Turks at home, is plodding determinedly away from the muscle- flexing of his predecessor, Andreas Papandreou. As for the Greeks, they are relieved that Mesut Yilmaz - another fine plodder - recently took over as Turkish Prime Minister from Necmettin Erbakan, whose Islamist inclinations meant that he was more interested in Libya than Greece.
The new configuration notched up its first success on 9 July, during a Nato summit in Madrid. Egged on by Madeleine Albright, Mr Simitis and Turkey's President Suleyman Demirel got together to talk about reducing tension between their countries. Theodoros Pangalos, Greece's Foreign Minister, and Ismail Cem, his Turkish counterpart, did the same. The result was the grand-sounding Madrid Accord, in which Turkey and Greece promised not to take up arms to resolve disputes in the Aegean Sea.
An important spur to better relations is Europe. Mr Simitis knows that being unkind to the Turks upsets his EU partners, who are fed up that Greece is blocking 375m ecus (pounds 260m) of funds earmarked for Turkey. As for Mr Yilmaz, he judges - correctly - that being friends with Greece will enhance Turkey's slim chances of EU membership. This view is shared by Mr Cem. On 18 July, the new foreign minister began his maiden press conference not with a traditional, anti-Athens broadside, but by suggesting that Turkey improve its dismal human rights record. He is supported by Turkish businessmen; they reckon bilateral trade - currently worth only $300,000 (pounds 185,000) a year - could rise to several billion if tension stays down.
The fly in the raki - or the ouzo - is Cyprus which also has aspirations to join the EU. But, there are signs of life there, too.
Earlier this month, the leaders of the Turkish and Greek areas met for the first time in three years. Yesterday, talks between Cyprus President Glafcos Clerides and Turkish Cypriot leader Rauf Denktash began at a luxury hotel overlooking Lake Geneva. The UN special envoy for Cyprus, Diego Cordovez said he did not expect the problem to be solved at the five-day meeting. Yet he was cautiously, pragmatically, optimistic.
"It will be different," he said. "We are changing the procedure. It has to be an incremental thing where you go slowly building an agreement. In the past, they started from zero and ended with zero. They started from zero trying to get one hundred."
But this will not be easy. On 16 July, the EU confirmed that it wants to begin negotiating Cypriot accession to the Union, which pleased the Greek Cypriot majority but infuriated the other side, which insists that Turkey be allowed in at the same time.
Never mind that the EU's decision had been expected, and that some EU members have said they will veto Cypriot accession unless the Turks agree; the EU's announcement has given voice to hawkish Turks - like Bulent Ecevit. An elderly nationalist with a famous mistrust for the EU, it was Mr Ecevit who ordered Turkish troops into Cyprus in 1974, after an Athens-inspired coup there threatened union with Greece. On 20 July, as Mr Yilmaz's new deputy prime minister, he announced that, rather than be shoehorned into the EU, Turkish Cyprus will "integrate partially" with Turkey. Last week, Turkey and northern Cyprus agreed to work towards partial integration, in an agreement which called for an Association Council.
The deal came under fire from Britain, America and others. They hope that Mr Ecevit will not influence Mr Yilmaz's policy of detente, nor further strain Turkey's relationship with the EU. If Mr Yilmaz gets his way, they hope, the thaw can continue.