The complex legacy of the alliance built to win World War II was on display in Red Square on Monday as world leaders gathered, at the invitation of Russian President Vladimir Putin, to mark the 60th anniversary of VE Day.

The event pays tribute to the immense Soviet sacrifice — the deaths of 27 million people, among them more than 18 million civilians — without which allied victory would have been inconceivable.

Yet, sitting in front of Lenin’s tomb, it is also impossible to avoid the brutal truth that the allied triumph placed much of Eastern Europe under Soviet control for nearly a half-century.

“World War II shows that in forming alliances, you often have to jump in bed with the devil,” University of Chicago political scientist John Mearsheimer, one of this country’s premier thinkers on international relations, told me. “We had to ally ourselves with Josef Stalin, one of the greatest mass murderers of all time.”

The leaders of the three Baltic republics that were swallowed up by the Soviet Union, two of whom refused to attend the ceremony, have reminded us of this less than honorable piece of Victory Europe Day (which Britain and United States commemorate on May 8). “On that day,” Lithuania’s president said, “we traded Hitler for Stalin and we should not celebrate it.”

President Bush is doing his best to straddle this dual legacy. He is bracketing the visit to Moscow with stops in the Baltics and Georgia, another former Soviet republic that has become a symbol of independence from Russian domination.

Bush should grasp as well the lesson that alliances almost always are imperfect, usually cumbersome, often involving painful compromise — and absolutely necessary.

This is a lesson the Bush administration still needs to learn. The president and his chief advisers are more comfortable without the encumbrances of alliance — witness their decision to refuse the offers of help from NATO during the Afghan War. They prefer to act unilaterally, rather than multilaterally. And even when they join with allies, it tends to be only on U.S. terms.

Undoubtedly, it is far easier to conduct war without having to take into account the domestic politics or the military commands of other nations. But as the aftermath of Iraq and Afghanistan have also made clear, the United States simply can’t run the world on its own.

That is even more evident as we confront other challenges in Iran and North Korea. These are problems that don’t lend themselves to purely military solutions. They require diplomacy in concert with allies — with the Europeans in dealing with Iran and with Asian allies such as South Korea and Japan.

And that’s not always an easy task. “The allies are more of a pain than ever before because they are no longer subservient to us,” said Stanford scholar Elizabeth Sherwood-Randall, a former deputy assistant defense secretary and author of a forthcoming book on alliance management.

Yet this is hardly unprecedented. Even a casual reading of the history of the Second World War reveals the often testy and complicated relations among the Big Three — Franklin Roosevelt, Winston Churchill and Stalin. There were constant tensions, attempts by each to play off one against the other and trade-offs of dubious morality, not least the decisions at Yalta to yield vast parts of Europe to de facto Soviet rule.

Alliances are by their nature a burden. “You pay a price in sovereignty, autonomy and freedom to maneuver,” said Sherwood-Randall, who managed defense relations with the former Soviet Union during the Clinton administration. “What you gain is legitimacy, capability and the sharing of burdens — blood and treasure, literally.”

One of the virtues of alliances, Mearsheimer pointed out, is that you can pass the buck. “You can get someone else to do the heavy lifting,” which in this case meant asking the Soviets to bear a horrible burden of casualties. Similarly, during the Cold War, if the United States had to contain the Soviet Union all by itself, “we would have had to maintain much larger military forces in Europe,” he said.

Churchill, in typical fashion, delivered the most famous one-line judgment on alliances. “There is at least one thing worse than fighting with allies,” the British leader said, “and that is to fight without them.”

Daniel Sneider is foreign affairs columnist for the San Jose Mercury News.