Many have warned that after the U.S. withdrawals from Iraq and Afghanistan, American-backed efforts to foster democratic government in both are likely to fail and Islamist radicals are likely to seize control of significant portions—if not all—of both countries. Meanwhile, some neighboring states hostile to American interests—especially Iran and Pakistan—are likely to take advantage of the situation. U.S. withdrawal from these two conflicts after sacrificing so many lives and spending so much money without achieving victory cannot help but encourage Islamist and other radicals elsewhere, as well as weaken America’s standing in the world. Yet for Washington to recommit the U.S. military in either conflict is untenable both politically and economically—not just for the Obama administration but even for a future Republican one.

So what is likely to happen following the U.S. withdrawals from Iraq and Afghanistan?

The position that the United States finds itself in today is reminiscent of the position it was in during the early 1970s. Back then, the country had become bogged down militarily not only in South Vietnam but also in Laos and Cambodia. The war effort had become highly unpopular both at home and in many countries throughout the world. Still, many warned that an American military withdrawal from Indochina would lead to negative consequences for the United States and for America’s standing in the world more generally.

Political and economic conditions inside the United States forced the Nixon administration to withdraw American forces from Indochina by the beginning of 1973. And many of the negative consequences predicted by those who wanted the United States to continue its war effort in Indochina did indeed come to pass. Communist forces overran South Vietnam, Cambodia and Laos in the spring of 1975. Further, the unwillingness of the American public and Congress to undertake military interventions elsewhere for fear of “another Vietnam” only encouraged Marxist revolutionaries—and their supporters in Moscow, Havana and elsewhere—to seize the moment. During the 1970s, Marxist revolutionaries succeeded in coming to power in several other countries, including Ethiopia, Guinea-Bissau, Mozambique, Angola, Afghanistan, and Nicaragua. Powerful Marxist insurgencies threatened to seize power in still other countries during the 1980s, including El Salvador and elsewhere in Central America, Peru and the Philippines. U.S. alliances appeared to be in tatters. There was a general sense that America’s power and influence were on the decline while the Soviet Union was on the rise.

By the early 1990s, however, the situation had completely changed. Soviet forces, which had invaded Afghanistan in 1979, withdrew in 1989 without having defeated the anti-Soviet insurgency. The communist regimes of Eastern Europe that were allied to Moscow all imploded in late 1989. Most Third World Marxist regimes either collapsed or realigned themselves with the West. At the end of 1991, the Soviet Union itself broke apart into fifteen separate countries. Friend and foe alike saw America as the winner of the Cold War and the sole remaining superpower.

This experience raises an intriguing possibility. The United States lost the war in Vietnam but went on to become the acknowledged winner of the Cold War less than two decades later. Could the United States also lose either the war in Afghanistan or Iraq and yet go on to win the war on terror as well? It is, of course, not inevitable that such a sequence of events will occur. But the fact that it occurred before raises the prospect that it could occur again. Withdrawal, then, need not lead to defeat. It may instead allow the United States to end the overextension that its opponents have taken advantage of up to now and better position the country to deal with any opponents that try to press their advantage and foolishly overextend themselves.

Mark N. Katz is a professor of government and politics at George Mason University and the author of Leaving without Losing: The War on Terror after Iraq and Afghanistan (Johns Hopkins University Press, 2012)