Like any arm of the US government that employs large men who wear moustaches and carry handguns on their belt, the FBI boasts the most macho of official mottos: "Fidelity, Bravery and Integrity".
If Clint Eastwood has his way, the nation's cinemagoers may soon be given to wonder if a fourth (and very different) abstract noun ought to be added to that proudly held list: Homosexuality.
The veteran film director will next month release a movie called J Edgar, which is billed as an extravagant biopic of the bureau's co-founder and director for 37 years of the 20th century, John Edgar Hoover.
It stars Leonardo DiCaprio in the title role, and a supporting cast that features Judi Dench and Naomi Watts. But that does not a hagiography make, and there are growing signs that the film will focus intently on suggestions that its supposedly conservative subject was in fact a closet gay.
Rumours about Hoover's close relationship with his aide Clyde Tolson have been circulating for years and are often explored by biographers. Outside the office, the duo, neither of whom married, were close lifelong friends, and frequently liked to holiday together.
When the great man died in 1972, the younger Tolson was named as his principal heir. And the two men chose to be buried within a few yards of each other, beneath the rolling lawns of the Congressional Cemetery in Washington DC. There are also reports, for now unsubstantiated, that both men privately enjoyed cross-dressing.
Historians are divided, however, as to whether they really were more than just friends. And admirers of Hoover - a right-leaning figure overly interested in the peccadillos of others, who supported some of the excesses of McCarthyism and was generally hostile to the civil rights movement - take great umbrage at those who cast aspersions as to his sexuality.
To that end, Mike Kortan, the FBI's assistant director, sent ripples of concern through his organisation last week when he revealed that both Eastwood and DiCaprio had sought information about Hoover's relationship with Tolson during briefings they were granted with officials from the bureau.
"We provided information so that their story could be accurate," he told USA Today. "What they did with it, as with any production, has been entirely in their hands."
Regarding the FBI's formal position on the matter, Mr Kortan added: "Vague rumours and fabrications have cropped up from time to time but there is no evidence in the historical record on this issue."
Behind the scenes, the forthcoming film appears to be the subject of growing controversy among the FBI rank and file. "There is no basis in fact for such a portrayal of Mr Hoover," William Branon, chairman of the J Edgar Hoover Foundation, is reported to have written in a letter to Eastwood: "It would be a grave injustice and monumental distortion to proceed with such a depiction, based on a completely unfounded and spurious assertion."
The Society of Former Special Agents of the FBI fired off a similar letter, according to USA Today, which first reported the controversy. That note said a "rumoured kissing scene", involving the actors portraying Hoover and Tolson, had "caused us to reassess our tacit approval of your film".
Eastwood replied in a joint letter with his producer Robert Lorenz. He said their film would give no "credence to cross-dressing allegations" and would not suggest that they were involved in an "open homosexual relationship".
However, it did not address the issue of whether the film would portray a closet homosexual relationship.
A synopsis says it will focus on "secrets" that Hoover hid "behind closed doors". But there is no indication as to whether those secrets concern such matters as his alleged links to the Mafia, or whether they involve matters of the flesh.
Intriguingly, Eastwood's screenwriter is Dustin Lance Black, who won an Oscar for the gay rights film Milk. And the J Edgar trailer contains a suggestive image of DiCaprio, as Hoover, clutching the hand of Tolson, played by Armie Hammer.
William Baker, a former FBI agent and Hoover foundation vice-president, denied that concerns over the film were rooted in homophobia. "We're caught in a dilemma," he said. "We don't want to support something not based in fact, but we're not against the new FBI and diverse workplace."