On September 21, 2001, the Federal Bureau of Investigation announced the arrest of Ana Belen Montes, a 43-year-old analyst at the Defense Intelligence Agency on charges of being a Cuban spy. Several weeks later the accused signed an agreement in which she pleaded guilty to one count of conspiracy to commit espionage, to submit to a debriefing by the FBI, and to serve a 25-year prison sentence. Montes — by this time the DIA’s top analyst on Cuba and a high-flier in intelligence circles — is the first major Cuban spy ever to be caught in America. “True Believer” (U.S. Naval Institute Press, 208 pages, $27.95) is the story of her career and the circumstances under which counter-intelligence officials were able to identify her and bring her to justice.

Sometime in the mid-1990s people at the DIA began to suspect that there was a leak somewhere in the building. But Montes was not at first a likely suspect. A quiet, disciplined, and productive intelligence officer highly regarded by her colleagues and superiors, she was born in Germany on a U.S. military base where her Puerto Rican father served as an Army psychiatrist. She received a first-class education in America, including an M.A. from the Johns Hopkins School of Advanced International Studies.

After a brief tour of the Justice Department, she joined the DIA and served there for 16 years. During that entire time she was meeting regularly meeting with her Cuban controller, often sending radio messages to Havana several times a week. This makes her one of the longest-running spies in American history, as well as one of the most thorough. At the time of her arrest, she was about to be loaned to the National Intelligence Council, the “cabinet” of the Central Intelligence Agency. It was only by some extremely fancy footwork that DIA spycatchers were able to prevent the transfer without arousing her suspicion while they closed their ring around her.

Given Montes’s extraordinary access to sensitive materials — and not just on Cuba or Central America — it is impossible to say just how much classified information was passed on to Havana (and from there to allies of the Castro regime far more dangerous to America). Much of it was crucial to U.S. operations in Central America and beyond. It seems likely that she was responsible for the death of one American serviceman on duty in El Salvador. Part of the book tells his story.

Scott Carmichael is a spycatcher with the DIA who spent five years pursuing his quarry, negotiating his way through what John le Carré once called a “wilderness of mirrors.” People like Mr. Carmichael have to operate on an unimaginably complex combination of social science techniques and ordinary human intuition. A good deal of guesswork and luck is involved. Sometimes there are serious struggles over bureaucratic turf, as in fact there was in this case. As the trap closes around the prey, most of the people involved with him or her must still be kept in the dark. And finally, there needs to be hard evidence. None of this came easily in case of Montes. She even passed a polygraph examination.

What leads people to betray their country? Obviously motives vary according to the individual. Most of the major security leaks in recent years in America — one thinks of the cases of John Walker, James Hall, Jonathan Pollard, and Ron Pelton — have been driven by financial need or greed. This was certainly not the case for Montes — she lived with extraordinary modesty. Her radio transmissions to Havana were directed from a small apartment in Northwest Washington. She did not own flashy cars or take expensive vacations. Nor was she driven by romantic or emotional reasons — there was no “honey trap” with some good-looking Cuban agent. Montes had an American boyfriend in Miami whom she saw on a regular basis. (An employee of another security agency, he was totally unaware of her secret life, as were her two siblings.) It appears rather that — like the Rosenbergs or Alger Hiss — she was driven largely by ideology, a sense of solidarity with Castro’s regime and its allies in Nicaragua and El Salvador. Indeed, she said as much in her plea agreement.

Mr. Carmichael ends his book on a disturbing note. He thinks many of his colleagues in the counterintelligence community tend to believe “the Cubans just got lucky with Ana Montes.” He argues, on the contrary, that Montes was the rule. “The true exceptions may be the hot-dog vendors, the lawn caretakers, and the other low-level agents whom the Cubans may employ inside or outside of our military bases.” “My fear,” he adds, “is that Cuban Intelligence is so good at their trade, they’ve recruited many Ana Monteses among us and planted those agents wherever they deem necessary within the U.S. government to advance their interests.” It is a sobering conclusion to a riveting story.

Mr. Falcoff is resident scholar emeritus at the American Enterprise Institute and author of “Cuba the Morning After: Confronting Castro’s Legacy” (AEI Press).