There’s already been one recent movie about San Francisco’s infamous late-sixties, early-seventies serial killer. But Alexander Bulkley’s bargain-basement, TV-quality “The Zodiac,” which made a brief stop in theatres before finding its way to cable and DVD, can’t hold a candle to David Fincher’s sprawling epic about the letter-writing, publicity-seeking murderer who was never caught and the effect he had on his pursuers in law enforcement and the media. (The two pictures actually have only two things in common—the fact-based storyline and the presence of Philip Baker Hall, who appears in both.) “Zodiac,” as Fincher’s article-less version is titled, is exquisitely crafted, well acted and surprisingly suspenseful, given the fact that it so faithfully—perhaps too faithfully—follows one thread of a narrative that’s very well known. It also presents a “solution” to the still-open case, based on the books by Robert Graysmith (who’s also a major character in the picture) that’s controversial, to say the least. But though “Zodiac” is structurally unwieldy and sags at times, as a whole it’s still a procedural with kick.

Fincher and screenwriter James Vanderbilt get the violence out of the way rather quickly, starting out literally with a bang by depicting what was probably Zodiac’s first kill, the shooting of a lover’s lane couple (Ciara Ferrin and Lee Norris), in which she’s killed and he’s badly wounded, and moving on with dispatch to his lakeside stabbing of another couple (Patrick Scott Lewis and Pell James) and his shooting of a San Francisco cab driver (Charles Schneider). But by that time his letters, complete with ciphers, have involved the staff of the San Francisco Chronicle—especially world-wise, alcoholic crime reporter Paul Avery (Robert Downey, Jr.) and geeky editorial cartoonist Graysmith (Jake Gyllenhaal), a single dad trying to care for his young son—and cops David Toschi (Mark Ruffalo) and William Armstrong (Anthony Edwards). After less than an hour, the picture has really settled into pure gumshoe mode, with—initially—the cops and the reporters operating largely independently of one another, and then, after the killings and letters have subsided, Graysmith becoming the focal point as he takes it upon himself to track down the killer with some unofficial help from Toschi, the cops from other areas where some of the killings occurred, and retired police handwriting expert Sherwood Morrill (Hall).

The first half of “Zodiac,” which is played out in short chronological segments precisely displayed in a parade of date-time-and-place subtitles, concentrates on the nuts-and-bolts efforts to unravel the killer’s messages and identify him. There’s a prime cameo here for Brian Cox as histrionic lawyer Melvin Belli, and he plays it to the hilt. Dermot Mulroney also gets a chance to shine as an S.F. police captain, and the interplay of jurisdictions—which could have been deadly dull—is actually made lively by Elias Koteas, an unusually serious Donal Logue, and (in the later stages) James Le Gros as policemen from outlying area. But despite the cops’ identification of one strong suspect, Arthur Leigh Allen (John Carroll Lynch), it doesn’t pan out, and the trail dries up as the killings and letters cease.

But that doesn’t stop Graysmith, who takes center stage in the film’s second half after Avery has descended into a self-destructive spiral and Toschi has to put the case on the back burner. The cartoonist’s obsession—in what seems entirely too conventional a turn—sours his relationship with his new wife (Chloe Sevigny) but eventually leads him back to the decidedly sinister Lynch, whom he fingers as the culprit in the book on which this script is based and presents an accusatory case against in a big monologue toward the film’s close.

There is, to be honest, a false sense of conclusiveness in this rather cut-and-dried finale. Graysmith (and Toschi before him) compiled a lot of circumstantial evidence against Allen, and it’s true that one of the survivors identified him from a picture as the attacker many years later. But there are some serious problems with the identification (which a recent DNA finding throws into question). Allen is actually rather like the Montague Druitt of the Zodiac case—a strong suspect whose guilt must still be considered “not proven.” And the sense of finality that the picture gives to its conclusion—which is really Graysmith’s—is excessive.

Of course, Fincher must have realized that it would have been too much to ask of an audience to follow such a tangled search over the course of more than 150 minutes, only to be sent home knee-deep in irresolution. And during the pursuit of this modern Jack the Ripper, Fincher and his expert collaborators—cinematographer Harris Savides, editor Angus Wall, composer David Shire, and the behind-the-scenes crew (production designer Donald Graham Burt, art director Keith Cunningham, costumer Casey Storm, and a small army of set designers and decorators)—work together not only to recreate the ambience of California in the sixties, seventies and eighties perfectly but also to fashion some wonderfully suspenseful sequences, even for those who know how they turn out. And that’s not just the case with the murders in the first hour—precisely the sort of thing in which one would expect the director to excel, and he does—but in later scenes, like the one in which a female motorist and her child are threatened by somebody who might be Zodiac, or the initial interrogation of Allen and a subsequent search of his trailer, and a passage toward the close in which Graysmith makes the mistake of visiting a decidedly peculiar movie buff (Charles Fleischer). The last is a show-stopper that would have made Hitchcock proud.

It’s also the capper to Gyllenhaal’s nimble performance as the twitchy, cerebral Graysmith. He and Downey—who makes Avery especially fascinating not merely with a nonchalantly oddball manner but by tossing off his lines so quietly that you often have to strain to hear them—rather overshadow the top-billed Ruffalo, who’s fine but doesn’t bring quite the last measure of charisma to a legendary lawman who served as a model for some of Hollywood’s most memorable cops (two of them—Bullitt and Dirty Harry—alluded to in the film itself). The supporting cast is strong down the line, with Lynch especially effective as the coolly menacing Allen.

There are points in “Zodiac” when you might feel that Fincher has become almost as obsessive as the real Graysmith about somehow including every twist and turn that marked this celebrated cold case over more than two decades. But if his complex yet elegantly straightforward combination of “All the President’s Men” and “L.A. Confidential” doesn’t quite match either of those models, it’s an atmospheric and mostly absorbing film in its own right.