On his trip to Europe this week, President Biden faced a question that he probably would have preferred to avoid: Should Ukraine be invited to join the North Atlantic Treaty Organization, and thereby receive a promise of mutual security from the United States as well as NATO’s other 29 members? (Biden responded that “it remains to be seen” whether this would happen but that Ukraine would have to meet certain criteria, including reducing corruption.)

Ukrainian President Volodymyr Zelensky, meanwhile, pressed Biden for a yes-or-no answer about the country’s bid in an interview with reporters. Several U.S. senators in the United States have again started to push the idea, which was first raised formally during the George W. Bush presidency — specifically at the 2008 NATO summit in Bucharest, Romania. The issue is undoubtedly often on the mind of Russian President Vladimir Putin, whom Biden is scheduled to meet with on Wednesday.

Inviting Ukraine to join NATO would be a significant strategic mistake. Bringing that nation — or another former Soviet republic, such as Georgia — into the alliance would not improve European security. Quite the contrary. It was one thing to offer membership to former members of the Warsaw Pact such as Poland (which joined in 1999) and even to former Soviet republics such as the Baltic states (2004); they had never been recognized by Washington as part of the U.S.S.R. It would be another thing entirely, and not a close call in terms of strategic wisdom, to include countries whose history and geography and people are so intertwined with those of Russia.

As the Greek historian Thucydides told us, human beings often go to war over pride. And few things could wound Russian pride more than this proposal for NATO expansion into the heart of the former Soviet space. Russia would surely respond with hostility — perhaps with deniable covert attacks that would make it hard for NATO to decide whether to respond yet leave Ukraine and/or Georgia at risk.

Of course, Moscow has no right to dictate events near its borders at the expense of its neighbors. There can be no “Yalta II,” whereby the great powers in effect divvy up Europe into respective spheres of influence, as happened at the end of World War II. The countries of Eastern Europe are fully sovereign and deserve every right to make their own domestic and foreign policy decisions. We in the West also owe a certain debt to Ukraine, which aided in global nonproliferation efforts when it gave up its nearly 2,000 nuclear warheads after the breakup of the Soviet Union in the early 1990s (in exchange for security guarantees from the United States, Britain, Russia and other countries — guarantees Russia has violated). That is why Ukraine deserves every right to join any other organization it wishes, should it qualify. For its part, Georgia has contributed troops in several difficult U.S.-led military missions over the past 20 years, including the wars in Iraq and Afghanistan. We owe them gratitude and help. But NATO membership is not the optimal tool for providing such help.

We need a new vision for Eastern European security. Our goal should be permanent nonalignment for Ukraine and Georgia, as well as Belarus and other countries that are not within NATO, such as Armenia and Azerbaijan, provided that Moscow make verifiable promises to end its aggression against its neighbors and allow them to join other organizations such as the European Union if they someday qualify. Regions such as the Donbas in Ukraine, where Russia has supported separatist violence since 2014, should gain a certain autonomy but remain within their current national borders. (Crimea, which Russia took from Ukraine in 2014, may need to be finessed; it is not clear there is a workable solution on this matter.) If Russia supports these ideas and implements them consistently, it should then benefit from a lifting of most Western sanctions.

NATO, an organization originally created by 12 countries bordering the North Atlantic region that grew to 16 by the Cold War’s end, is large enough already. It has nearly doubled in membership since the Berlin Wall fell. It is often mistakenly viewed at least as much as a tool of democracy promotion globally rather than one intended to preserve core Western security interests. Rather than enlarge it even more, with predictable and indeed inevitable consequences for the U.S.-Russia relationship, we need a new vision for this part of Eurasia. An alternative geopolitical solution would place real demands on Russia’s behavior yet also seek to avoid the exacerbation of tensions in an already very fraught relationship.