A “glimmer of hope” but “no illusion” was the inauspicious way Angela Merkel, the German chancellor, described the Ukraine cease-fire she and President François Hollande of France brokered in talks in Minsk, Belarus, with Presidents Vladimir Putin of Russia and Petro Poroshenko of Ukraine. Ms. Merkel certainly deserves a lot of credit for her determined shuttling among Kiev, Moscow, Munich, Washington and Minsk in the urgent search for a resolution of the biggest security crisis to confront Europe since the end of the Cold War.

The last cease-fire negotiated in Minsk, in September, quickly unraveled, and the new one is very limited, leaving hard problems to be settled in coming weeks and months. And in the end, it is still for Mr. Putin to decide whether this is to be a real step toward peace or just another cynical feint in his campaign to dismember Ukraine.

Mr. Putin won a lot in Minsk. The fact that the cease-fire is to start on Sunday — and not immediately, as the Ukrainians wanted — gives the Ukrainian separatists a couple more days to press their siege on Debaltseve, a key rail hub where thousands of Ukrainian troops are surrounded, and in their attack on the Black Sea port of Mariupol. If the cease-fire does take hold, which is far from certain, both sides are to pull their heavy weapons out of range of each other. Then the deal requires both sides to withdraw “foreign” fighters and equipment, though Mr. Putin has never acknowledged the obvious presence of Russian forces and weapons in eastern Ukraine.

On the political side, the agreement says Ukraine can recover full control over its border with Russia by the end of 2015, after local elections in rebel-held areas and constitutional changes that would give these areas considerable autonomy. The degree of self-rule for pro-Russian regions of eastern Ukraine is at the core of any sustainable settlement, but the negotiations will take place while Russia remains free to move men and equipment over the border.