The Kurdish problem is everybody's problem, but above all mine," said Turkey's Prime Minister Recep Tayyip Erdogan in the mainly Kurdish city of Diyarbekir last week.
"We will solve all problems through democracy," he added - and went on to admit that the national Government, dominated by the Turkish-speaking majority, had long mistreated the Kurds, who make up a fifth of the country's people.
The rebel Kurdistan Workers' Party (PKK), which resumed its separatist war in south-eastern Turkey last year after a five-year ceasefire, responded immediately by suspending all attacks for a month.
Can it be as simple as that? Well, no, but the words must be said. Kurds suffered more than anyone in the PKK's separatist revolt from 1984 to 1999, which killed 37,000 people.
Most of them don't insist on a separate state; they just want respect for their language and culture in a country that once denied their very existence.
But Erdogan had to convince them he was truly committed to righting past injustices, so they needed a public apology.
The trick now will be to turn the PKK's one-month unilateral ceasefire into a permanent peace. That mainly depends on Erdogan persuading Turkish public opinion and his own armed forces to let the PKK participate peacefully in legal, democratic politics.
The situation is similar in Indonesia, where the separatist rebels in Aceh province signed a peace deal with the Government on August 15 after a 29-year war that killed at least 15,000 people.
What opened the door to peace was the tsunami last December that gave both sides a new perspective, but the words still had to be said there, too.
They were spoken first by the rebels of the Free Aceh Movement (GAM), who announced last February that they would finally drop their demand for independence if the Indonesian state would live up to its long-neglected promises of local autonomy for Aceh.
The new Indonesian president, Susilo Bambang Yudhoyono, had already been making conciliatory noises, so Finnish President Martti Ahtisaari's Crisis Management Initiative offered mediation and, after five rounds of negotiations in Helsinki, they came up with a peace deal that may work.
GAM's 3000 fighters will disarm under amnesty, while its leaders will re-emerge as a legitimate political party. The local government will get a high degree of autonomy, including 70 per cent of the income generated by the province's rich oil and gas resources, and Jakarta will withdraw more than half of its 53,000 troops and police from Aceh. And everyone will live grumpily ever after.
Even the most embittered conflicts over language, religion and ethnicity are soluble if there is enough patience and goodwill.
The past month has seen another case where a peace settlement that almost fell apart was saved, at least for the moment, by people who simply refused to lose their heads or to jostle for political position. The Sudan peace deal is still holding, despite the unexpected death in a helicopter crash of its main architect, John Garang.
It's enough to restore your faith in the concept of enlightened self-interest.
Once conflicts topple into organised violence, the rules of war generally force people to behave like intransigent fools. That doesn't mean they really are, and given a chance they can behave sensibly. Democracy often gives them that chance.
Look around: rational behaviour abounds. Not just in Turkey and Indonesia and Sudan.
Sub-Comandante Marcos has just led his Zapatista rebels out of the Chiapas jungle with a view to influencing Mexico's next election. The IRA's spokesman, "P. O'Neill", declared last month that the IRA "has formally ordered an end to the armed campaign. All IRA units have been ordered to dump arms."
And the incentive, every time, is the prospect that the rebels can achieve the more important of their goals through democratic political action.
* Gwynne Dyer is a London-based independent journalist.
<EM>Gwynne Dyer:</EM> How saying the right words can save lives
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