Why Ukraine truce works for both sides
The ceasefire deal announced for eastern Ukraine has the potential to become a turning point - all sides have welcomed it as a possible first step towards peace.
So what motivated both the Russian and Ukrainian presidents to step back from the brink, besides the mutually avowed aim of doing all they could to stop the bloodshed and suffering?
There's no doubt Ukrainian President Petro Poroshenko's options were limited.
If he was hoping for a swift campaign to crush the rebels in the east so he could get on with the business of pulling Ukraine out of its economic mess, then in the last two weeks he must have realised he would not be allowed to.
A recent injection of manpower and heavy weaponry - presumably from Russia - meant the pro-Russian rebels, from being on the back foot, were able to open up new fronts and in places force Ukrainian troops into an abrupt and humiliating retreat.
The reaction in Kiev was ill-concealed panic. In President Poroshenko's own words, it looked like "direct and open Russian aggression".
The message - one assumes delivered to President Poroshenko's face when President Putin met him two weeks ago in Minsk - was that Ukraine will not be permitted to win this war in the east.
The Ukrainian government should never forget that Russia will always have the power to mount a counter offensive, or simply keep the region perpetually unstable - hampering Mr Poroshenko's plans for nationwide parliamentary elections next month.
And how could elections take place when the emergency in the east was leading the Ukrainian government to talk of imposing martial law?
Besides, President Poroshenko must have been left with few illusions about Western military aid. As this Nato summit made clear, when you strip back the tough anti-Russian rhetoric, the West is pragmatic and circumspect when it comes to Russia.
Yes, it is prepared to back Kiev politically, economically and to help it with advice, training and non-lethal assistance. But Ukraine is not in Nato, and the West is not prepared to go to war with Russia over it.
As French and German leaders have said repeatedly in the past few weeks, in the end, this Ukraine conflict will end with a ceasefire. In other words, it is up to you, Mr Poroshenko, whether it is sooner or later.
But if Ukraine was boxed in and had few options, what about Russia? Why would President Vladimir Putin stop now?
He could have pushed his advantage in eastern Ukraine (as Russian conservative nationalists had been hoping) to annex the territory, declare it part of Russia, or a new Novorossiya territory under Russian protection, and create a useful land bridge to Crimea.
The fact is, Mr Putin had ample chance to take over eastern Ukraine if he had wanted. But it is not clear what advantage taking over the territory would bring him.
It is poor, many of its industries are loss-making, the local population is traumatised and divided. And it would be a messy bloody fight, involving large number of Russian troops, and who knows how many Russian casualties.
And that may well be a risk Mr Putin is not prepared to take.
Already reports of Russian soldiers killed in eastern Ukraine and brought home for secret burials have caused ripples in Russian society. Attempts to report on the funerals were, it seems, at first hushed up.
But in this age of social media, on a subject of such acute interest to so many families in Russia, it is impossible to stop rumours from spreading. The influential Soldiers' Mothers Committee has weighed in, urging parents to check that their sons are not being sent to Ukraine.
It is interesting that now Russia's state-run TV is beginning to acknowledge the presence of Russian volunteer fighters in eastern Ukraine, some of them serving soldiers, some of them special forces, and some of them losing their lives. It is a recognition of the sensitivity of this subject.
A mission in eastern Ukraine resulting in many young conscripts shipped home in body bags could be disastrous for the Russian president. His near god-like status could quite quickly be eroded if Russians felt their sons were dying for no good purpose.
Much better to try to stop the conflict now, sue for peace from a position where the rebels have some military advantage and the Ukrainian government is looking vulnerable, and hope for a peace deal that will deliver Russia's key demands.
Is this the only reason? Western sanctions, too may be playing their part - not least because reportedly prices are rising in Russia, especially for food - something that poorer members of the population will feel at once.
In the end, for both presidents, it is probably domestic pressure that weighs most heavily on them and determines how they choose to act.