For a day and half at Reykjavik, Iceland, in October 1986, Ronald Reagan thought that he and Mikhail Gorbachev "were going to achieve something remarkable" -- an agreement to eliminate all ballistic missiles from the arsenals of the United States and the Soviet Union.

And then, Reagan recalled, "Gorbachev threw us a curve. I realized he had brought me to Iceland with one purpose" -- to kill the Strategic Defense Initiative. "The price was high but I wouldn't sell."

Six months later, according to Martin Anderson (an economic policy adviser in the Reagan White House) and Annelise Anderson (associate director in Reagan's Office of Management and Budget), "the Soviets caved."

Gorbachev agreed to sign a treaty eliminating intermediate-range nuclear weapons from Europe.

In their third Reagan book, the Andersons draw on his speeches, diaries and recently declassified minutes of National Security Council meetings to celebrate "the old duffer" as a visionary who won the Cold War by crafting a peace-through-strength foreign policy that brought the world a giant step closer to nuclear disarmament.

The Andersons demonstrate, conclusively, that Reagan had a deep and abiding commitment to abolish nuclear weapons. And that he viewed SDI ("Star Wars") as a defensive system that could render those weapons "impotent and obsolete."

"Reagan's Secret War," however, is more hagiography than it is history. Depending almost entirely on Reagan's rhetoric and his recommendations, the Andersons' analysis of arms negotiations is incomplete and inaccurate.

Consider, for example, their view of the "zero-zero option," which eliminated American and Soviet intermediate-range ballistic missiles in Europe as a bold, indeed a revolutionary, proposal. It wasn't.

"Zero-zero," Pulitzer-Prize winning historian Richard Rhodes has demonstrated, was designed by Assistant Secretary of Defense Richard Perle to look like a reasonable bargain to everyone but the Soviets.

The Andersons do not indicate that the deal required the Soviets to give up all its weapons, including newly deployed SS-20s, while the United States pledged merely to get rid of old missiles it planned to eliminate anyway and not replace them with new ones.

"Zero-zero" left British and French nuclear assets intact. Nor did it touch bombers or sea-launched missiles, areas where the United States had a substantial advantage.

The Andersons never doubt the sincerity of American negotiators. Like Reagan, they see "Star Wars" as an insurance policy for the world and seem to believe that the United States might have agreed to share the technology with the Soviets.

And they dismiss every Soviet proposal as a propaganda ploy concocted by a desperate regime.

For almost half a century, the leaders of the United States and the Soviet were "apes on a treadmill," marching belligerently in no particular direction.

Reagan deserves credit for recognizing that by feeding the arms race, "deterrence" threatened to destroy what it was supposed to protect.

But then again, so does Gorbachev. After all, he pushed for the 50 percent reduction in strategic forces that became the basis for the historic agreement that followed the "might have been" at Reykjavik.

Gorbachev's critique of SDI, moreover, was anything but irrational. If deployed, it would make a "first strike" tempting -- and unleash a new arms race on Earth and in space.

The Andersons' Reagan is too smart, too consistent, too prescient, to be true. All too often, in their book, he's a heroic character in a Grade B movie, refusing to rest until he's spared the world from the scourge of nuclear weapons.

In real life, the president was more contradictory and complex than that. Capable, at times, of self-deprecation and self-knowledge, you can almost imagine him reading "Reagan's Secret War" and asking, "Where's the rest of me?"