The British electorate’s stunning vote to leave the European Union has been followed by predictions in the United States about the dire consequences of this choice. The fate of the global economy and peace itself are said to be at risk, along with the ability of the United States to deal with Russia, Islamic terrorism and other problems while undercut by a weakened EU and a UK turned inward as it undergoes a decade-long process of unwinding its European ties.

Such alarms are highly overblown. Young Europeans are not about to begin slaughtering each other in the manner of their great-grandfathers, and the claim that they will or might shows how threadbare the argument for the European project has become. In eastern Europe, war is a possibility, but it is one that the EU has failed to avert and, as in the current conflict in Ukraine, arguably has helped to create. The claim that recession in Britain will drag down the world economy is also far-fetched. The eurozone has long weighed on global growth, presenting a problem that needs to be tackled no matter what the outcome of the Brexit vote.

While it is true that disentangling the UK from the EU will take time, here as well the difficulties are overstated. Unlike in the United States, where federal law applies directly to citizens and corporate entities, EU federalism operates through the member states, which transpose union laws into national law. British legislation based on EU law will remain in place, with the proviso that Parliament now will be able to amend or repeal such laws without being taken to the European Court of Justice.

If much American commentary on the consequences of Brexit is overwrought, there is, however, one sense in which it is greatly understating the magnitude of what happened on June 23. Brexit is a shattering blow to an American policy that for more than sixty years has operated on the theory that “more Europe” was always possible, always desirable and always good for the United States. This theory is now in tatters, and U.S. policymakers must deal with its shambolic aftermath. Historic nation-states, and not just the UK, are at risk of breaking up. The EU itself is badly weakened, devoid of the sense of purpose that motivated its founders. A new basis must be found for relations between the United States and the UK, which, unless action is taken, will find itself with less access to the American market and fewer avenues of cooperation with the American people than those enjoyed by countries geographically and culturally more distant and far less central to U.S. interests.

U.S. policy did not cause the current shambles, but it contributed mightily to it through the single-minded pursuit of an approach to Europe that rejected any alternative to integration along the lines propounded in Brussels. We have reached the end of a long road to nowhere. U.S. policymakers now must adopt a new and more flexible mindset.

Dean Acheson, the greatest of the postwar secretaries of state, was also perhaps the last to take a pragmatic, commonsense view of European integration. He supported European unity to the extent that the Europeans themselves wanted it, but he was sympathetic to the need of the battered nations of Europe to rebuild their identities after World War II, and declined to use the Marshall Plan or NATO to compel the Europeans to unite, as even then advocates of the “dumbbell” model of Atlantic relations were urging. As he wrote in his memoirs, he was skeptical of Jean Monnet’s “fanatical zeal for supranational points of view.”

This changed after Acheson. The Republicans under Eisenhower were still shedding the isolationism that had made them fierce opponents of aid to Britain and France against Hitler. A federal Europe was the magic bullet that would make unnecessary the permanent stationing of U.S. troops in Europe. Reinforced by his own admiration for Monnet, John Foster Dulles backed the ill-fated European Defense Community long after it had any chance of becoming a reality. While enthusiastically supporting the Common Market, notwithstanding the economic discrimination that lay at the heart of the enterprise, Dulles declined to back a British proposal for a wider European Free Trade Agreement intended to head off the UK’s isolation from the continent.

The Kennedy administration was even more single-minded in its pursuit of integration along federalist lines. Led by Under Secretary of State George W. Ball, Monnet’s American lobbyist and lawyer, the United States pressured the UK to apply for membership in the European Community. The administration expunged the “Atlantic Community” from its vocabulary in favor of an “Atlantic Partnership,” said to be composed of two equals, the United States and an enlarged EC. To advance the partnership, the administration proposed special U.S.-EC trade arrangements and cooked up a crazy scheme, the Multilateral Nuclear Force, which it was hoped would promote the federation of Europe and encourage Britain and France to abandon their national nuclear arsenals. In the end the EC rejected the trade agreement, the MLF collapsed under its own weight and French president Charles de Gaulle vetoed Britain’s bid for EC membership.

The Johnson administration picked up the pieces of what Ball had called the “Grand Design” by reforming NATO and patching relations with Britain and West Germany. Richard Nixon and Henry Kissinger later sought to inject a new flexibility into U.S. policy by building bridges to de Gaulle. But patterns had been set, de Gaulle soon left the scene and Kissinger was frustrated in his attempt to negotiate a “New Atlantic Charter.” Subsequent administrations came to support any advance on integration emanating from Brussels, a trend that reached its apogee in the post–Cold War 1990s, as the United States urged the EU to expand faster and further to the east and southeast and cheered on the march to the disastrous euro.

This era is now over. There is no going back to the past, although it is worth asking whether any of the alternative orders that the United States so fiercely opposed—some variant of de Gaulle’s Europe des patries or of Harold Macmillan’s European Free Trade Area—might have been preferable to the outcome we now have. The original Europe of the Six, now threatened by the likes of Geert Wilders and Marine Le Pen, might have progressed to a genuine federal union with all its advantages. Beyond, a looser, more differentiated area would have muted the existential importance of “in” versus “out.” There might have been less need for the centralized bureaucracy that the voters so detest. Russia, a European country that finds no place in Europe, could have been accommodated more easily following the collapse of communism.

But all this is food for historical speculation. Today, there is much that needs to be done.

The economic agencies of the U.S. government should be in overdrive. Setting the terms for UK-EU trade in the post-Brexit world is not a strictly bilateral matter, and still less a unilateral decision by which the EU dictates the terms of divorce. Trade agreements concluded by the EU and the UK are subject to WTO rules, and post-Brexit arrangements must not result in market access for the United States or other third parties worse than those currently in force and established by bargaining in the Uruguay round and previous GATT rounds. The United States should not take sides in the EU-UK negotiations on political grounds, but President Obama’s vow that the UK must go to “the back of the queue” clearly must be dropped. If it proves advantageous to negotiate a free trade agreement with the UK and London is interested, Washington should go for it, much as it has with Chile, Israel and any number of other countries.

The United States needs to reengage with NATO, a process already underway in response to tensions with Russia. The old quad mechanism within the alliance of the United States, UK, France and Germany could be reactivated, possibly with enlargement to Italy and Poland.

Washington should look for opportunities to enhance its foreign-policy and security dialogue with Europe, the prospects for which might improve with Britain out of the Union. Cooperation between the EU and NATO has long been hampered by fear in Europe about its supposed threat to the EU’s foreign-policy autonomy. Dialogue might actually be enhanced in a forum that includes the United States, Britain, the EU (however it chose to be represented), Canada and someday, it is to be hoped, a less hostile and more democratic Russia.

The United States needs to stop pressing the EU to enlarge, especially to Turkey. The voters clearly do not want it, and to insist that they must accept it against their will is to risk further damage to the EU while doing nothing for Turkey. The same logic must apply to Moldova, Ukraine, Georgia and any number of other countries that pose challenges, which at various times U.S. officials have hoped could be “solved” through the deus ex machina of EU accession.