In 1992’s Prime Suspect, Helen Mirren’s portrayal of British police detective Jane Tennison as an intelligent, overworked, embittered drone was a revelation, not least of all because this potentially depressing character was so endlessly interesting — prickly yet likable, victimized by sexism yet never a victim.

Prime Suspect’s theme of thwarted prejudice never got in the way of its tense murder-story plot, and now Mystery!: Prime Suspect II, a new four-part sequel, attempts to raise the stakes on every level — there’s a grislier, more complicated murder case, with racial politics added to sexism as subtexts.

In Prime Suspect II, the skeleton of an African-Caribbean woman is discovered, a coroner deems the death a murder, and Mirren’s Detective Chief Inspector Tennison puzzles over who killed her and why. The case becomes a flashpoint for the angry middle-class minority neighborhood in which the body was found. The solution to the murder becomes, for the area residents, a politically charged metaphor for the amount of attention the government will pay to them. Tennison is under pressure, therefore, to solve the case as quickly as possible, and the temptation for her and her police detective unit to make quick, hasty judgments is enormous.

It is this portrait of a woman under the gun — symbolically and, as a police officer, sometimes literally — at which Mirren excels. She allows us to identify with her tough challenge and her exhaustion even as we exult in the crisp, canny way she goes about interrogating suspects and piecing clues together. Mirren knows that there’s something deeply satisfying — quietly thrilling — about watching someone do her job well, and in the best moments of Prime Suspect II, we’re on Tennison’s wavelength, never privy to more information than she has, as she moves inexorably toward wrapping up this messy case.

Mirren’s achievement is strong and clear, but the script is more problematic. Working from a story provided by Prime Suspect I author Lynda La Plante, writer Allan Cubitt is laboring at a disadvantage. In the first Suspect, Tennison was struggling not only for the respect of her male colleagues but for the survival of her job on the police force as well. In the sequel, she’s pretty firmly in control, and she’s fighting for a promotion — a worthy goal, to be sure, but not quite as do-or-die as her previous dilemma. Perhaps as a result, Cubitt, who also wrote the excellent recent Masterpiece Theatre entry The Countess Alice, has chosen to distract us regularly from this thin plot line with a meatier one — Tennison’s interactions with one of her officers, Detective Sgt. Oswalde (Colin Salmon), an African-Caribbean colleague with whom Tennison has had a brief fling.

The duo’s interaction in the office is strained because of their personal bond, but rather than explore the unique intricacies of these personalities, Cubitt frequently reduces the relationship to a series of social quandaries: a white woman dealing with a black man; a boss romantically involved with her subordinate. When, in Part 2 of Prime Suspect II, Oswalde tries to draw parallels between their situation as minorities within the white male power structure of the police department, telling Tennison, ”I’m the same as you,” the remark is intended as a stark, emotional high point, but it falls flat from sheer obviousness.

Prime Suspect II works best in small ways, when it’s closest to honoring the conventions of traditional detective fiction. The best scene in this miniseries, directed by John Strickland, is an artful variation on a standard murder-mystery device, the deathbed confession. In this one, Tennison tries to coax the admission of murder out of an ailing, morose racist played by Tom Watson. As Tennison perches on the edge of this hateful man’s bed, she must mask her disgust with compassion, worried that the old coot will have another heart attack before she squeezes the information out of him. She decides to be soothing, purring with insistence that he has to come clean to her. These few moments — a showcase for both Mirren and Watson — contain more suspense than anything else in Prime Suspect II.

Similarly, there is also enormous pleasure to be taken in the tiniest shadings of Tennison’s character — the way, for example, she’s made even crankier than usual by the fact that she’s trying to give up smoking and instead chews grumpily on endless sticks of gum. Mirren has already signed to do a third edition of Prime Suspect. Despite her career as a feature-film actress (White Nights; The Cook, The Thief, His Wife & Her Lover), she obviously knows that TV’s Jane Tennison is a great role. And despite the fact that Prime Suspect II isn’t as strong as the original, it’s still comparable with the best cop shows on American TV. There’s no reason not to await Prime Suspect III with eagerness. B+