"Covert Affairs" (Tuesdays, 10-11 p.m. EDT, on USA) falls into the category of unexpected pleasures—always wonderful to encounter but a touch suspect. There was plenty to raise suspicion in the flimsy premise of this series about a late-twentysomething beauty, Annie Walker (Piper Perabo), who decides, after a shattered romance, to join the CIA—where else would you go to heal a broken heart? Still the premiere episode, which aired in July (directed by Tim Matheson), was so effective, polished and layered with intriguing suggestion—including echoes, pathetically welcome, of the late "24"—it dispatched all sense of the flimsy, and ventured nowhere near the standard paranoid murk of dramas about the CIA.

Christopher Gorham and Piper Perabo as CIA agents in 'Covert Affairs.' Steve Wilkie/USA Network

It promised, in short, steadily absorbing plots and skilled writing, and these the series has delivered ever since—whether in the episode on an IRA terror mission to the U.S., or the one on terror funding in Latin America, or, last Tuesday, on Annie's adventures in Zurich. Next week's episode, on Sudanese arms dealing, guest stars Gregory Itzin, that old "24" hand.

Sharply drawn characters people this fictional CIA world, among them Arthur Campbell (Peter Gallagher), head of Clandestine Services for the CIA, and his wife, Joan (Kari Matchett), head of the CIA's Domestic Protection Division and a superbly menacing presence. She leads the list of reasons the atmosphere of the CIA offices is so evocative of "24"—there's something of the same sense of duplicity and danger, the strong suggestion of a trusted insider up to no good. Even the marital counseling sessions the Campbells undergo carry an air of large menace—larger than the personal issues confronting this couple, the main one being infidelity. There's no better clue to the series' sly wit than its poker-faced detail about Joan Campbell's use of an agency tracking device to spy on her husband, who is, she's grimly certain, having an affair. It's the answer to every suspicious wife's dream—the power of the CIA to uncover what the sneak is up to.

For all that, the characters never stray into the farcical, or any roles other than the dead-serious ones they've been assigned: They're the CIA, charged with protecting the national security, and no less urgent about their missions than the officials at Jack Bauer's old CTU. The show's creators (it was executive produced by Doug Liman of the Bourne trilogy) maintain a steady hand—what they're up to is drama and as much suspense as they can extract. They don't make the mistake, ruinous to so much adventure drama, both in television and film, of undermining themselves with forays into the cute and the comic.

That's not to say there aren't perky moments and plenty of badinage, most of them involving Annie—one episode has her warding off grapplings from a 20-year-old with a crush—but they're neatly folded into the action. Annie has left her heart in Sri Lanka, where she woke up after a blissful night, abandoned by the man she considered the love of her life, who has left a cryptic goodbye note.

She gets to work hard as a CIA trainee, but not for very long—the agency has plans for her, though not the kind she imagined. As she tells her CIA boss when she arrives, she'd spent time helping out after the uprising in South Ossetia. Just what they need, Joan Campbell mutters, "a bleeding heart." But Annie speaks six languages—talents that make her desirable to the CIA. One of her early assignments is to pass herself off as a prostitute, in the interest of obtaining intel.

Annie, dressed in tailored black jacket and white shirt, wants to know if she should change her clothes. She's fine, her boss assures her—hookers in D.C. are pretty conservative. She gets considerably more counseling on vital matters from her agency ally, Auggie Anderson, a blind CIA military agent, a character charmingly underplayed by Christopher Gorham. His Auggie is one of the relatively few blind characters in film who can sound persuasively casual.

There is precious little of the casual either in character or story in this series, blazing with action. The chief clue to the quality of the show in episode one came with the ferocious action set in a hotel room—an assassination attempt nearly perfect in its echoes of the high-tech mayhem of "24." At the center of every one of these violent engagements, whether car chase or hand-to-hand combat, is Ms. Perabo's redoubtable Annie—a hero who manages, like Jack Bauer himself, to withstand the most extraordinary battering with hardly a mark to show for it. That's if we don't count the one ostentatious result of a battering Annie has survived—great big runs in her stockings, on which the cameras linger.

"Covert Affairs" is, of course, never going to be "24"—but, four episodes into this series, its pleasures are no longer the unexpected kind.

Write to Dorothy Rabinowitz at dorothy.rabinowitz@wsj.com