Good question–but one without a simple or easy answer. Ever since U.S. nuclear-attack plans were codified into a Single Integrated Operating Plan (SIOP) in 1960, presidents have been appalled by the very notion of having one day to open the nuclear “football” and transmit the “execute order” (for years, the code words were “Red Dot”). After President Kennedy was briefed on the SIOP, he muttered, “And we call ourselves the human race.” But no president has ever figured out a better way.

Now, a decade after the cold war, Bush wants to try. Last Saturday, during his two-hour “get to know you” meeting with Russian leader Vladimir Putin, Bush began the difficult and delicate task of discussing how the former rival superpowers, which still have at least 12,000 nuclear weapons aimed at each other, might begin to reduce their arsenals. Bush and Putin didn’t get into specifics, but the mood between the two men seemed surprisingly warm. Bush even invited Putin, a man he said he could “trust,” to his Texas ranch, saying that “friends don’t destroy each other.”

With Russia strapped for cash and its nuclear arsenal rotting and rusting, the time seems right for both sides to cut back on nuclear overkill left over from the cold war. Bush appears genuinely committed to what he called “rethinking the unthinkable” –to finding ways to “take nuclear weapons out of our relationship with Russia,” as a top aide puts it. With or without Russia, Bush seems more determined than his predecessors to actually make deep cuts in the nuclear arsenal. But the president’s task is complicated by the top item on his foreign-policy agenda: missile defense.

Missile defense is intended not to defang Russia but to deter rogue states from trying to blackmail the United States with a nuclear-tipped rocket or two. But the Russians, understandably, don’t quite see it that way. Nor do many others. For months Bush has been flayed by editorial pages in the United States and Europe for pushing a plan that, his critics argue, will “destabilize” the old balance of terror and stimulate a new arms race. For decades, both superpowers relied on the doctrine of mutually assured destruction, or MAD, to deter a nuclear war. The idea was to make a first strike suicidal by guaranteeing that the other side would be able to hit back. The threat of a shield that could intercept their missiles–and so, in theory, make Russia vulnerable to a first strike–could make the Kremlin resistant to deep cuts in its nuclear forces. And China, which has only a small nuclear arsenal, might feel impelled to build a bigger one.

Or so the argument goes. Bush devoted much of last week’s European trip to touting his missile-defense plan, but it actually would be decades, if ever, before the United States could build a system strong enough to withstand even a small missile barrage. Moscow’s anxiety about missile defense might be allayed with the right sort of incentives, i.e., investment by the West. Russia is also worried about its decaying arsenal, which is increasingly blind to attack and scarily kept on a hair trigger. Last week Putin at least acknowledged the need for a “new architecture of security.”

A bigger impediment to President Bush’s dream of reducing the U.S. nuclear arsenal may be his own Pentagon. America’s nuclear-force structure is like a Rubik’s Cube, deceptively difficult to dismantle. That’s what Dick Cheney found out in the spring of 1989, a few weeks after he had taken over as secretary of Defense for Bush’s father. Cheney was given a slide show on the SIOP, 60 to 100 images laying out the sequence of strikes planned in a nuclear war. Each strike was represented by a red dot. At its cold-war height in the mid-’80s, there were 16,000 Soviet targets in the SIOP database. By 1989 the number had shrunk to 12,500. Even so, close to 500 warheads were targeted on the Moscow area alone. A single anti-missile radar at Pushkino, northeast of Moscow, was targeted with 69 warheads. Cheney watched, dumbstruck, as the red dots metastasized across the Soviet Union. Finally, he said, “Who ordered all this?” The Air Force chief of staff, Gen. Larry Welch, answered, “You did, sir. You and your predecessors.”

The general meant that the military was merely carrying out the orders of its civilian masters to fulfill the logic of MAD. Maybe so, but the doomsday planners have been pretty literal-minded. Cheney actually tried to whittle down the SIOP. The 12,500-target list was cut to 10,000. One of the bright stars of the Air Force, Gen. George (Lee) Butler, was sent to Omaha to run the Strategic Command and found the SIOP to be “all ‘Alice in Wonderland’ stuff.” Every time the Pentagon bought a new weapons system to match the Soviets, the generals needed to add new targets for the new weapons, until they were aiming at targets as small and insignificant as rural railroad sidings. Butler took an ax to the SIOP. Yet, bizarrely, the SIOP is actually 20 percent larger today than it was after Butler had finished. His successors kept adding targets back in.

To control the military and bring down nuclear forces to, say, 1,000 weapons or less, Bush is going to have to give precise marching orders. That may mean confronting a painful reality: targeting Russian cities in order to maintain deterrence. Knocking out Russia’s scattered silos and other nuclear targets requires more than a thousand warheads. A single Trident submarine, on the other hand, could devastate Russia by unleashing the 192 warheads on its missiles on Russian cities. Nuclear-war planners have always argued that targeting missile silos and command centers is more “humane.” It is a somewhat bogus argument–as the accompanying graphic shows, millions of Russian civilians would still die. But no president, including Bush, is going to feel comfortable explicitly aiming at the Russian population.

To help work through this dilemma, Defense Secretary Donald Rumsfeld has brought back General Butler as a consultant and tapped Richard Perle, a veteran of the Reagan administration who has radical views on nuclear weapons. It may take considerable prodding to move the top brass. A preliminary review of America’s nuclear posture, ordered up by Rumsfeld a few months ago, is “a disappointing document, wholly without vision,” says a knowledgeable source. In an interview with NEWSWEEK before he was lured back to the Pentagon as an adviser, Perle said, “I see no reason why we can’t go well below 1,000. I want the lowest number possible, under the tightest control possible.” Why? “The truth is we are never going to use them. The Russians aren’t going to use theirs either.” Perle accepts the truth of what Kennedy’s national-security adviser McGeorge Bundy–himself no dove–wrote in 1969: that in the real world, “even one hydrogen bomb on one city” would be “a catastrophic blunder; ten bombs on ten cities would be a disaster beyond history.” No doubt true. But to persuade both sides to truly reduce their arsenals will take a degree of leadership not seen since the superpowers developed the capacity to make the rubble bounce.