In late 2000, the FBI was closing in on a suspected spy for Cuba working inside the Defense Intelligence Agency. Undercover operatives would soon begin trailing Ana Montes, the agency’s top military and political analyst on Cuba, by car and on foot. They filmed her making calls on pay phones, even though she carried a cellphone in her purse. They intercepted Montes’s mail and inspected the trash outside her apartment in Washington.

Montes had been spying nearly 17 years for Cuba, passing along so much classified information about DIA personnel, as well as on eavesdropping technology covertly installed on the island, that she essentially compromised every method the United States used to surveil the Castro regime, according to current and former U.S. intelligence officials. That makes Montes one of the most damaging spies of her time, they said.

Opening an investigation against a decorated intelligence officer, who colleagues heralded as the “Queen of Cuba,” was painstaking and high-stakes. And almost as soon it began, the FBI nearly shot itself in the foot.

The slip-up was inadvertent. Whenever the bureau began an intelligence investigation that might ruffle feathers in a foreign government or upset U.S. foreign policy, officials typically informed the State Department’s Office of Foreign Missions (OFM). It was a sleepy outfit, responsible for keeping tabs on travel by foreign diplomats and overseeing such things as plans to build new embassies or consulates in the United States. Hardly the setting for an espionage thriller.

So Terry Holstad, then the chief of the Cuba unit at FBI headquarters, never thought twice when he described the secretive Montes investigation to the bureau’s liaison to the OFM, a veteran agent and longtime colleague named Robert Hanssen.

Unbeknown to Holstad and the rest of the FBI, Hanssen had started spying for Russia more than 20 years earlier. He gave thousands of pages of classified documents to the KGB, divulging secrets about U.S. nuclear war planning and weapons technology. He compromised the identities of dozens of human sources, at least three of whom were executed, according to a review by the Justice Department’s inspector general, which called Hanssen “the most damaging spy in FBI history.”

Following Hanssen’s arrest in February 2001, Holstad remembered telling him about the Montes case only a few months earlier.

“I said, ‘Oh, my God, I wonder if he passed the information to the Russians,’” Holstad recalled in a recent interview. He said he can’t remember if he used Montes’s name. But the details of the case were particular enough that if Hanssen had tipped off Moscow, the Russians might have told the Cubans, who ran a world-class intelligence service. And if they warned Montes, she might have fled the country.

The precarious twist in the Montes case was discovered and detailed in a new book by investigative journalist Jim Popkin. He has written extensively about Montes, whom he called “the most important spy you’ve never heard of” in a 2013 feature for The Washington Post.

The Post obtained a copy of the book, “Code Name Blue Wren: The True Story of America’s Most Dangerous Female Spy — and the Sister She Betrayed,” which will be published in early January — days before Montes is scheduled for release from a federal prison in Fort Worth.

“Holstad said the months after Hanssen’s arrest were excruciating because Ana still was walking free,” Popkin writes.

Holstad said he spent hours interviewing Hanssen in jail in Virginia and later in a supermax prison in Colorado as part of a team convened by the CIA to assess the damage Hanssen’s espionage had caused. Though Hanssen confessed to spying for Russia, he denied alerting his handlers to the FBI’s investigation of a Cuban spy, Holstad said, and claimed that he was only interested in providing information concerning Russia.

“I don’t believe his denial,” Holstad told The Post. “He was very narcissistic. If he believed he could enhance his reputation by passing this on, he would have.”

The end to Montes’s espionage career was precipitated in part by the Sept. 11, 2001, terrorist attacks. The DIA was preparing to assign Montes to a team that would have access to information about locations the United States might bomb in Afghanistan. The FBI already had enough evidence to arrest her. Retired Vice Adm. Thomas Wilson, then the DIA director, told Popkin that he called the bureau and demanded they take Montes off the street.

On Sept. 21, 2001, Montes was arrested at DIA headquarters and escorted out of the building in handcuffs. Senior Cuban government officials publicly praised Montes and saluted her work, portraying her as a fellow warrior in their fight for socialism and against the Reagan administration’s backing of anti-communist rebels in Nicaragua.

The CIA took a dimmer view. In a still-classified psychological assessment, Popkin reports, the agency concluded that while Montes had not volunteered to become a spy, she didn’t hesitate after the Cubans propositioned her. Montes’s handlers made her believe she was indispensable to their cause, “empowering her and stroking her narcissism.”

An unrepentant Montes rejected the suggestion that the Cubans had manipulated her.

After Popkin’s article was published in The Post, Montes wrote to a friend, who shared her letter with the journalist. Montes “mocked” the story, Popkin writes in his book, and said “she would much have preferred a clinical analysis of why she spied, with a history lesson for readers on the U.S. attempts to ‘unjustly overthrow the government of Nicaragua in the 1980s,’ and other examples of what American administrations have done to foreign countries from the nineteenth century to today. In Ana’s recounting, gone would be any personal accountability, replaced by fact-laden stories of American hostility and imperialism worldwide.”

If she emerges from prison in January, Montes may have the opportunity to more fully account for her actions. Hanssen, who may or may not have revealed her secrets, will have no such chance. Now 78, he is serving a sentence of life in prison without the possibility of parole.