On May 9th, Vladimir Putin is gonna be overseeing a parade in Moscow’s Red Square, commemorating the Soviet Union’s victory in the Second World War. It’s like an annual display of military bravado that, since Russia’s full-scale invasion of Ukraine in 2022, has taken on more explicit political undertones. The country’s like triumph over Nazism is presented as proof of its righteousness in the current war—and of its role as a global power. Last year, as intercontinental ballistic missiles capable of carrying nuclear warheads rolled across the square, Putin linked the “radiant memory” of those who gave up their lives in the Second World War with “our brothers-in-arms who have fallen in the struggle against neo-Nazism and in the righteous fight for Russia”—that is, Russian soldiers killed in the current war in Ukraine.

This year, the celebrations in Moscow serve another purpose: a way for Putin to show that he is not geopolitically isolated—China’s Xi Jinping and Brazil’s Luiz Inácio Lula da Silva are expected to attend. In recent weeks, Donald Trump has called for a thirty-day ceasefire as a step toward ending the war in Ukraine, a proposal to which the Ukrainian President, Volodymyr Zelensky, has agreed. Putin countered with a three-day ceasefire over the May 9th celebrations, a way to protect the Russian capital from Ukrainian drone strikes and to give Trump just enough so that he doesn’t lose interest or, worse, blame Putin for hampering his peacemaking efforts.

“Putin is trying to walk a thin line,” Thomas Graham, a fellow at the Council on Foreign Relations, who served as a top White House adviser on Russia during the George W. Bush Administration, said. “He doesn’t want to offer any concessions on Ukraine, but he also wants to keep the U.S. engaged.” Trump’s intent to deliver a speedy end to the war in Ukraine has led to a dynamic in which Putin and Zelensky are competing to make each other the subject of Trump’s ire. “If Trump’s attempts at mediation fail, what matters is who will he find guilty: Moscow’s stubbornness or Kyiv’s reluctance to agree to his terms?” a Moscow foreign-policy source told me. “Both sides are staging a play for an audience of one.”

As a result, both leaders have been forced to make adjustments. Putin, for example, began with an insistence that the U.S. pressure Zelensky to step down as Ukrainian President, that Russia would only deal with his successor or, as Putin suggested in March, a U.N.-led “transitional administration.” For a moment, Trump seemed receptive to the idea, calling Zelensky a “dictator” and labeling him, not Putin, as the intransigent party in the negotiations.

But holding elections in Ukraine would be a complicated and drawn-out process; Trump wants a faster deal. Eventually, Putin’s focus on removing Zelensky led to a rare rebuke from Trump, who, in late March, said that he was “very angry” and “pissed off” by Putin’s demand. Since then, Putin’s precondition has steadily melded into a recognition that, for the moment, Zelensky isn’t going anywhere, and Russia can’t use that fact as a reason not to engage with Trump on the question of ending the war. Recently, Putin’s spokesperson, Dmitry Peskov, called “legal issues related to legitimacy” of Zelensky’s Presidency a “secondary” concern. “The Kremlin has functionally admitted it is ready to deal with the existing political regime in Kyiv,” the Moscow foreign-policy source told me.

Yet Putin and others, including Foreign Minister Sergey Lavrov, have made it clear that any agreement must address the so-called “root causes” of the war: a list of grievances that stretches from NATO’s expansion eastward in the nineteen-nineties to the provision of Western arms to Ukraine. In an interview with CBS News last month, Lavrov spoke of “direct military threats to Russia just on our borders” and, in a moment of grim irony, the “human rights” of ethnic Russians and Russian speakers in Ukraine—code for Russia’s historic claim on Ukraine itself.

From the outset, Putin saw the invasion as a way of forcing a larger conversation with the West on Russia’s terms, in which the whole of Europe’s postwar security architecture would be relitigated. Graham, who travelled to Moscow in February for informal talks with Russian officials and experts, told me, “From Russia’s perspective, there isn’t a solution to the war that doesn’t contain a broader understanding of how European security will be handled in the future.” Putin has not given up on this goal; if anything, Trump’s conciliatory disposition toward Russia’s claims—“I think what caused the war to start was when they started talking about joining NATO,” Trump said of Ukraine during a recent interview with Time—has made this prospect appear more achievable than ever. “President Trump is probably the only leader on earth who recognized the need to address the root causes of this situation,” Lavrov told CBS.

The talk of these root causes is a way to widen the aperture of U.S.-Russia relations, with the ultimate goal a kind of Yalta 2.0, Putin’s ambition of many years, in which Washington and Moscow soberly divide up the world, coöperating on issues of global importance and ceding zones of influence in each other’s backyards. “The Russian side has tried to diversify the number of subjects on the agenda: ‘Let’s talk about diplomatic relations, coöperation in the Arctic or in space, the Iran track,’ ” the Moscow foreign-policy source said. “It’s all part of an attempt to show Trump that relations between Moscow and Washington can include much more than just Ukraine.”

At times, Trump appeared interested. He suggested restoring Russia as a member of the G-8; his phone calls with Putin have veered from Ukraine into subjects as wide-ranging as global energy markets, the role of the dollar, and artificial intelligence. His envoy, Steve Witkoff, has developed a clear affection for Putin, calling him “gracious,” “smart,” and “not a bad guy.” During an interview with Tucker Carlson, in March, he spoke of the “so-called five territories” in Ukraine that Russia has annexed as part of Moscow’s rightful dominion. “There have been referendums where the overwhelming majority of the people have indicated that they want to be under Russian rule,” Witkoff said.

That creates an incentive for Putin to keep the momentum going. “If the U.S. leaves, all these efforts to pull America into a larger conversation in which two great powers solve the problems of the world likely falls apart,” Tatiana Stanovaya, a senior fellow at the Carnegie Russia Eurasia Center, said. For Putin, Stanovaya went on, “too much of what he wants to achieve is now tied up with Ukraine negotiations, which means he’s been forced to rethink his position—not about his larger war aims, but how he pursues them here and now.”

In the opposite case, if no deal is reached and Russia is not blamed for the failure, the U.S. might abandon Ukraine entirely. That scenario would be even more advantageous for Putin, who puts little merit in Ukraine’s own defense or Europe’s ability to fill in the gaps. “He believes the Americans simply need to get out and then it’s only a matter of time before Ukraine throws in the towel,” Stanovaya said. The war will continue to extract a cost on Russia’s resources—including dead soldiers, lost equipment, and unsustainable budget expenditures—but “Putin is sure history is on his side, so he can’t imagine any other outcome than Ukraine’s resolve dissolving sooner or later and Russia getting what it wants, or rather, deserves.”

Regardless of which scenario comes to pass, Putin has every incentive to drag out the process. According to Western estimates, Russia is using large cash bonuses to recruit as many as thirty or forty thousand new troops a month. Russia’s military expenditures are increasing faster than those of all European countries combined. Russia is ramping up long-range drone and missile production, for example, while Ukraine’s stockpiles of missiles for its air-defense systems are running low. “There’s a feeling in Moscow that time is on our side,” the foreign-policy source said, “that our negotiating position will only strengthen over the next weeks and months.”

Of late, there have been some signs that Trump is willing to increase the pressure on Putin, even if in a rather toothless nature. In late April, after Russia launched its largest barrage of drones and missiles in months, killing at least twelve people in an apartment building in Kyiv, Trump declared on Truth Social, “Vladimir, STOP!” The trick for Putin is to not actually stop, while also playing for time. “On the one hand, the Russian side thinks the longer it haggles, the more concessions it can get,” the Moscow foreign-policy source said. “But, on the other, there is indeed a fear that Trump’s patience cannot last forever, and we don’t want to end up on the wrong side of it.”

Senator Lindsey Graham, a Trump ally, has put together a sanctions package that would target countries that purchase Russian oil, a broad measure aimed to undercut the Kremlin’s oil revenues, which, together with the gas trade, provides for a third of the country’s budget. Graham positions the bill as punishment for Russia not making peace; Trump has said that his signature “depends on whether or not Russia is behaving.” Alexandra Prokopenko, an expert on Russian economic and monetary policy at the Carnegie Russia Eurasia Center, told me that, for Putin, losses from new sanctions would be painful but, as she put it, “not apocalyptic.” She explained, “Three years of sanctions have proven the adaptability of the Russian economy to all manner of external shocks.”

Zelensky, meanwhile, is guided by a similar principle as Putin: don’t be the problem. On the sidelines of Pope Francis’s funeral on April 26th, he appeared to make some headway in persuading Trump that Putin was causing the holdup in the ceasefire negotiations. Afterward, Trump declared that maybe Putin “doesn’t want to stop the war, he’s just tapping me along, and has to be dealt with differently.”

That was a stark contrast from Trump’s tone during a disastrous Oval Office meeting with Zelensky, in February, during which Trump bellowed, “You don’t have the cards,” and threatened to pull U.S. aid, saying, “I don’t think it’s going to be pretty.” The U.S. suspended military and intelligence assistance for a week. Trump said that it has been “more difficult, frankly, to deal with Ukraine” than Russia.

“There was a big feeling of sympathy for Zelensky,” a European foreign-policy official told me. “But we also sent Ukraine a clear message that they need to mend fences with the U.S.—it’s a dangerous illusion for them to think they can go on without them.”

“We learned our lesson,” Alyona Getmanchuk, director of the New Europe Center in Kyiv, said of the Oval Office meeting. “Our strategy now is to avoid saying no.” She brought up the example of the U.S.-Ukraine minerals deal, which was signed in Washington on April 30th. (The deal was meant to be signed in February, but the ceremony was cancelled after the blowup between Zelensky and Trump.) The Trump Administration initially pushed for five hundred billion dollars in mineral wealth, billed as debt repayment for U.S. military assistance since the start of the war. In the end, the mention of past debts disappeared. But Ukrainian officials did not manage to insert specific mention of security guarantees, a top priority of Zelensky’s. The deal is more symbolic than substantive. Still, considering how bad things looked for Kyiv some weeks ago, the signing of a deal is a clear diplomatic victory. “We should apply this model to other issues on which we’re still not on the same page,” Getmanchuk said.

One part of Trump’s would-be peace plan is that the U.S. will recognize Russia’s annexation of Crimea. “Crimea will stay with Russia,” Trump told Time. “And Zelensky understands that.” Formally, no Ukrainian President could ever agree to give up territory—that is constitutionally impossible and politically suicidal—but it’s possible to imagine de-facto workarounds. For starters, the U.S. can make such a declaration on its own. “I think it would be a mistake for the Americans to recognize Crimea,” the European foreign-policy official said, “but they don’t need the Ukrainians to sign up to that.”

Maksym Skrypchenko, the head of the Transatlantic Dialogue Center, a think tank in Kyiv, who was recently in Washington for talks with U.S. officials, said that Ukraine could, for example, commit to stopping strikes in Crimea as part of a ceasefire agreement. “The Russians may call that recognition,” he told me. “We would consider that honoring a ceasefire agreement.” As for security guarantees, Skrypchenko suggested a model in which European financial assistance could be used to purchase U.S. weaponry. “The direction of travel is pretty clear,” the European official told me. The notion of a significant contingent of troops from a European-led coalition on the ground in Ukraine, what Zelensky and other officials continue to push for, is “not likely to happen”—as much as European capitals may posture, they won’t agree to such a mission without meaningful support from the U.S., which looks to be a non-starter. Instead, the official said, European states “will need to quite substantially subsidize Ukraine’s armed forces.”

Zelensky is a proud and headstrong leader who also faces democratic pressures at home. (He clearly hopes to retain power when Ukraine holds elections, a process that could begin with a stable ceasefire in place.) There’s a chance that Trump’s efforts lead both sides, one step at a time, to project a willingness to make peace that ends up turning into the real thing. “It’s possible that, in the end, two parties looking to avoid blame above all leads them to end up with a workable deal, almost by accident,” Skrypchenko said. Still, the incentive for Zelensky to avoid Trump’s wrath can only stretch so far. “Ukraine can’t agree to a plan in which the victims are punished for being victimized,” Getmanchuk said.

But, as the European official pointed out, Zelensky’s quibbles and proposed tweaks to Trump’s peace initiatives are of a specific, tactical nature: a revision here, a counterproposal there. More fundamentally, Trump wants a ceasefire first, talks on ending the war later—a position to which Ukraine has accommodated itself. Russia wants the opposite: talks about everything up front, and only then can the war come to an end. Sooner or later, the official went on, that may lead Trump and Putin into a more sweeping, and strategic, dead end. “Putin simply doesn’t want what Trump wants”—that is, a lasting peace in Ukraine, to close off the conflict as it stands now. “That’s the fundamental difference,” the official said. “Ukraine wants the war to stop and Russia doesn’t.”