In late 1974, someone slipped a note under the door of the Soviet Embassy in Washington. "Certain authorities of the United States," the anonymous author claimed, "are taking measures to raise the Soviet submarine sunk in the Pacific Ocean." The note was signed simply: "Well-wisher."

Anatoly Dobrynin, the Soviet ambassador to Washington, reported the warning to Moscow and demanded an explanation from Secretary of State Henry Kissinger—"we cannot be indifferent to any operation of raising any parts and property of the submarine." The submarine being referred to was K-129, which had gone down in 1968 in the north Pacific. For the Soviets the sinking of the sub was both a tragedy—six sailors were lost—and a potential intelligence disaster: K-129 carried operations manuals, codebooks and nuclear weapons.

The only solace for the Soviets at the time was their confident belief that the U.S. would never find K-129—they themselves had repeatedly failed to do so—much less raise it from the deepest beds of the Pacific Ocean. But by the time the note from "Well-wisher" arrived at the Soviet Embassy, an American attempt to recover the sub was already under way, in what has to count as one of the oddest episodes of the Cold War.

David Sharp's "The CIA's Greatest Operation" is the story of Project Azorian, the code name given to the CIA's covert recovery mission. The engineering challenge was daunting, to say the least: to locate the sunken sub; find a way to hoist it to the surface; and to do so in utter secrecy in waters three miles deep. There was no precedent for such an operation. Mr. Sharp details the myriad ideas that went nowhere until a workable plan was agreed upon.

The Glomar Explorer, built in secret to recover a Russian submarine. Courtesy of the Central Intelligence Agency

In the end, the project would take six years, from the first stages of planning to the mission's conclusion in 1974, and cost hundreds of millions of dollars. It would require a custom-built recovery ship, a mechanical claw that weighed four million pounds, a lifting pipe weighing twice that, and a complex system of hydraulics. And, of course, Azorian would require a flawless cover story or, as Mr. Sharp prefers to call it, "the best lie"—in this case the claim that the busy American ships in the northern Pacific were mining manganese. Given the tensions of the time, Moscow's discovery of the mission might have sparked a naval confrontation. One State Department official went so far as to warn that Azorian could trigger a third world war.

Mr. Sharp, who served as director of recovery systems for Project Azorian, says that he was compelled to write "The CIA's Greatest Operation" because the truth has been mangled by other writers and because the CIA has shrouded the mission in secrecy for too long, robbing the participants of the honors they deserve. Mr. Sharp is among the last surviving members of the CIA team. "If I didn't write the story, who would be left to tell it?"

The CIA's Greatest Covert Operation

By David H. Sharp

Kansas, 328 pages, $34.95

It's a fair question and a noble goal, and Mr. Sharp has clearly worked hard to gather every shred of information from the episode. Unfortunately, his passion and effort aren't matched by a gift for storytelling. The writing is engineer-friendly, perhaps, but largely misses the drama of the tale. He writes of "lubricity additives" and "davit actuator seals," of "snubbers" and "gimbals." There are too many sentences like this one: "The counterweight was designed to compensate for the tilting moment applied to the gimbaled rig floor by the transfer boom." When Mr. Sharp gets to the heart of the mission, he resorts to excerpts from the recovery vessel's daily logs. It's a dry way to handle the most compelling turns in the narrative.

Still, Mr. Sharp brings a trove of fascinating material to his account. Soviet vessels shadow the recovery ship, the Glomar Explorer, hoping to divine more about what the Americans are up to; at one point Soviet sailors, looking for clues, pick through trash bags that the Glomar crew has tossed overboard. There is a stirring moment—almost like a lunar landing but on the ocean floor—when the sub first comes into view, by way of a closed-circuit camera. Fans of Cold War history won't soon forget the solemn burial at sea the CIA men give the K-129 submariners, nor one truly bizarre exchange between Americans and Soviets at the scene. Mr. Sharp tells us that when the Soviet salvage tug SB-10 passed the Glomar at less than 50 yards, its entire crew "lined up on the rail and mooned." The Americans stared "in disbelief" and then returned the greeting.

Beyond engineers and intelligence officers, Project Azorian drew in Mr. Kissinger, Brent Scowcroft and a young Donald Rumsfeld. Mission orders reached the desks of Presidents Nixon and Ford. There are cameos from Howard Hughes, whose company built the Glomar Explorer, and John Wayne, who lobbied the White House not to scrap the vessel, which he called "one of the most imaginative vehicles of all time." He was right about that.

Was the mission a success? All of K-129 was indeed lifted from the ocean floor, but roughly two-thirds of it fell away on its way to the surface and was never recovered. And what intelligence did the mission gather? To this day the results remain classified—but we know that some nuclear torpedoes were in the portion of the sub that was retrieved and that the bulk of what the Americans were looking for was left underwater. The Soviets didn't learn the extent and true nature of the mission until Robert Gates, then head of the CIA, met Yeltsin in 1992 and told him about the Soviet sailors that the U.S. had found and buried at sea. "Perhaps the mission was truly impossible," Mr. Sharp concludes, though he also quotes the ship's security officer saying, "What man could do, we did."

—Mr. Nagorski is a managing editor at ABC News and the author of "Miracles on the Water: The Heroic Survivors of a World War II U-Boat Attack."