On April 7, a war between Russia and NATO forces defending the three Baltic republics was avoided by just twenty feet. A senior Estonian official explained to me in vivid detail how on that day a Russian Su-27 fighter jet buzzed a US military plane over the Baltic Sea, only veering off after coming within twenty feet of causing a mid-air collision. Such an event could have prompted retaliation by NATO and possibly given Moscow a pretext for invading Estonia (population 1.2 million), where a few NATO planes are now based.

Several times a month since the conflict in Ukraine began, Russian jets have been buzzing Western military and civilian flights over the North Sea and as far off as the English Channel and the Atlantic. The European Leadership Network (ELN), a non-profit research group devoted to European security, has recorded dozens of close military encounters between Russian fighter jets and Western planes since the Russian annexation of Crimea in March 2014, a majority of them over the Baltic Sea. At least eleven were described as “serious incidents of a more aggressive or unusually provocative nature.” Some of these incidents, like the April 7 near miss, had a “high probability of causing casualties or a direct military confrontation between Russia and Western states.”

These incidents have occurred across Europe and near the coast of the United States and Canada. In March 2014, a Russian reconnaissance plane with its transponder turned off nearly collided with an SAS passenger plane fifty miles southeast of Malmo, Sweden. “A collision was apparently avoided thanks only to good visibility and the alertness of the passenger plane pilots,” the ELN found. And last summer, an armed Russian fighter flew within ten meters of a Swedish surveillance plane flying in international airspace between Sweden and Latvia.

For the three tiny Baltic republics of Estonia, Latvia, and Lithuania, the situation is particularly unnerving. Russian fighter jets based in Kaliningrad can be over Baltic airspace within minutes of takeoff, leaving hardly any time for air traffic controllers to respond. And many Russian military planes fly with their electronic transponders, which make them easy to track, switched off. With no sign of the confrontation between Russia and the West over Ukraine coming to an end, what most frightens the peoples of Estonia, Latvia, and Lithuania is not war by design but war by accident.

NATO officials at last month’s annual security conference in Tallinn, the Estonian capital, made no bones of the fact that they were being challenged in the air by Russian President Putin almost every day, and that Russia was essentially leaving it up to them to take precautions to make sure there was no accident. One official described some Russian pilots as almost kamikaze in their reckless fly-bys of NATO planes and forays into Baltic airspace. According to the ELN, Latvia has recorded more than 150 incidents of Russian planes approaching its airspace since March 2014, while Estonia has recorded numerous Russian violations of its airspace in the same period.

The three Baltic republics have a combined population of just six million people. They have the highest standard of living among the former states of the Soviet Union with a per capita income of nearly US $27,000; and they are also the only former Soviet states to become members of the European Union and the European currency union. They are model states for democracy, respect for human rights, and transparency, and have among the highest rates of Internet access in the world.

But the mood in all three countries is dark. At the Tallinn conference, Baltic presidents and NATO officials were unusually blunt in describing the extent to which the security architecture in Eastern Europe has collapsed, how Russia poses the gravest threat to peace since World War II, and how the conflict in Ukraine and the loss of the Crimea has left the Baltic states on the front line of an increasingly hostile standoff. Amid these tensions, the thought of a plane crash leading to war seems scarily plausible.

As if this were not enough to worry about, there was also discussion of nuclear weapons. In recent years, Russia’s defense budget has increased some 50 percent, with a large chunk of it going to nuclear weapons. Russian President Vladimir Putin has made clear that Russia’s annexation of Crimea could be defended by both nuclear and conventional military means, and at the Tallinn conference, Radosław Sikorski, the Marshal of the Polish parliament, said that Russia’s military strategy appears to have changed to allow the first use of nuclear weapons.

Others spoke of the influence on Russian public opinion of the Kremlin’s portrayal of the conflict in Ukraine, which it describes as a Western military aggression against a pro-Russian population that must be met with Russian force if necessary. As a result, nuclear weapons have once again become an acceptable part of the debate in Russia, with Russian TV bolstering the idea of nukes just being one more tool in the Russian arsenal. One official told me that new opinion polls in Russia show that large numbers of Russians are ready to discuss the possibility of nuclear war with the West and that some 40 percent of young people believe that Russia could win a nuclear war with the US and Europe.

In fact, as NATO Deputy Secretary General Alexander Vershbow made clear, NATO has been taking Russia’s nuclear threats quite seriously for some time and has also been preparing countermeasures, including ways to pre-empt Russian use of small scale tactical nuclear weapons, which Russia might consider as a strategy to end the war on Russian terms while avoiding an all-out nuclear war. For example, some participants in the discussion in Tallinn outlined a scenario in which Russia might threaten to use nuclear weapons over a dispute such as Ukraine or an invasion of the Baltic states, but then might ultimately choose to use a tactical weapon with a small blast range on a European city or a Western tank division. Vershbow himself was so blunt that the moderator Nik Gowing of the BBC had to check constantly that his comments were on the record.

Being from Pakistan, I tend to be more concerned about the spread of the Islamic extremism than the spread of the new Russian empire. But I was struck nevertheless that the new rhetoric that is emerging from Russia about nuclear weapons—including statements in the Russian media last year that Russia is “the only country in the world capable of turning the USA into radioactive dust”—is in some ways as chilling as the Islamic State discussing the annihilation of all Shia Muslims and minorities such as the Yazidis in the Middle East.

For now, though, the greatest threat may come from Russian fighter jets. It’s not clear that NATO has a strategy for dealing with these everyday provocations. To some extent, NATO forces can meet the Russian incursions by scrambling their own jets and making clear it is ready to defend Baltic airspace. In 2014, for example, it conducted over one hundred intercepts of Russian aircraft, triple the number of the previous year; nearly seventy “hot” identification and interdiction missions were conducted off the coast of Latvia alone. Talks, trade sanctions, bluster, and appeasement have all been tried at one time or another and nothing has worked with Putin. This week, NATO sent a thousand troops to take part in the largest military exercises ever staged by Estonia. But Baltic leaders also want the US to permanently deploy more military forces in Eastern Europe, and Washington has been reluctant to do that.

Meanwhile, the deliberate Russian near misses continue, and it is largely up to the Western planes, caught be surprise, to simply get out of the way.