Set in Washington, D.C., Paul Schrader’s latest character study, “The Walker,” sometimes possesses the quiet and stately hush of gentility — except, of course, when the wives of men in power are dealing risqué gossip over canasta. The movie’s opening shot, a slow pan over the card room’s gold-brocaded walls, suggests the importance of surface appearances, but it also evokes the secret toll of humiliations and compromises inflicted on the women’s eponymous companion. “The Walker” is about Carter Page III (Woody Harrelson), a gay man who elegantly accompanies these lunching ladies at cards and outings, and who upholds a sense of decency and loyalty that proves old-fashioned. Mr. Schrader, best known for his screenwriting credits on such hits as “Taxi Driver” and “The Last Temptation of Christ,” traces Carter’s gradual decline when he refuses to implicate a confidante whose lover, a lobbyist, is found murdered. Until the movie’s enigmatic mood dissipates, it holds our interest for a surprisingly long time through a pervasive sense of loneliness and Carter’s dignified, gloomy resignation.

Some of the surprise comes from Mr. Harrelson, who holds his own as Carter, or “Car” as he is known. After years of the one-time “Cheers” bartender playing gap-toothed country boys or some species of macho boob, “The Walker” seats him at a country-club table to trade bon mots with Lauren Bacall, Lily Tomlin, and Kristin Scott Thomas (as his closest friend, Lynn). Impeccably attired in high-collared suit and tie, demurely mustachioed, his Carter is restrained, knowing, trusted, but still as cautious as an outsider.

Car gains some automatic respect as the son of a famous congressman (his namesake), but “The Walker” seems to underline breaks with the past, contrary to the old-fashioned ring of the escort role. Instead of following in his father’s footsteps, Car appears to work a day or two at a boutique realty office, while his fickle boyfriend Emek (Moritz Bleibtreu) crafts art out of Abu Ghraib photos. And of the government that buzzes behind the social scenes that Car frequents, we hear often that the men in charge are a different sort, merciless, even ruthless, “since 9/11.”

Since Car was the first on the murder scene, he soon comes up against one hardliner, an obnoxious investigating attorney named Mungo Tenant (William Hope). As Car delves into the matter, he crosses paths with his friends’ husbands, powerful men all. An unreadable senator (Willem Dafoe) foots Car’s legal bills for questionable reasons, and later a venal politico (Ned Beatty, playing a corrupt oldster again, as in the recent “Shooter”) informs him he’s on “the wrong side of history.”

Ever conscious of keeping the machinery of polite society running smoothly, Car cleans out his desk at work, even before he’s asked, soon after he begins to be investigated. Without explicitly showing as much, “The Walker” is filled with the implied sound of doors slowly being closed and wagons being circled, as people genteelly calculate the trajectory and the dangers of the latest scandal. Throughout, a tight-lipped Car patiently upholds his code of gentility beyond what his friends might deem necessary (though he tries to explain his behavior: “I’m not naïve. I’m superficial”).

Mr. Schrader steers “The Walker” carefully, but as a murder mystery — complete with a foot chase — creaks into action, the movie starts to lose its fraught atmosphere. But, as is typical of Mr. Schrader’s films, such as “American Gigolo,” “Auto Focus,” and even his remake of the “Exorcist” prequel, classical care has been taken with expressive shot-framing and production design. (Indeed, “The Walker” shares more than a passing resemblance to “American Gigolo,” which tells the story of a male escort who is put in jeopardy by the rich and powerful following a murder he didn’t commit.) Car’s discovery of the murder victim is credibly tense with a clenched sense of shock. The attorney’s questioning rooms are eerily theatrical, and Car’s apartment is a closed-off sanctuary of red brocade and chinoiserie.

In the end, “The Walker” is indelibly a Schrader film for the sheer intensity of its character scrutiny, even when we know exactly, and tragically, where everything must be headed. And if not to the extent of Mr. Schrader’s “Affliction” and its ragged star, Nick Nolte, “The Walker” is palpably aided by Mr. Harrelson’s lead performance. The actor yields a deeply affecting vulnerability, and even in the film’s final scene, a too-explicit statement of his predicament, we fully feel Car’s wounded nobility in the capital’s unforgiving wilderness.