One might be inclined to call Paul Weitz’s film a comedy-drama, but though it has some serious undertones, “Admission” is basically a straight-on comedy—one that’s less broad and raunchy than today’s run-of-the-mill, age-of-Apatow laughfests, to be sure, and somewhat more sophisticated. But in the end it’s much less clever than one might hope, a film based on a couple of slender premises that earn an occasional chuckle but little more.

It’s also hobbled by its leads, both of whom basically repeat their familiar shtick rather than offering anything new or inventive. Tina Fey plays Portia Nathan, a longtime admissions counselor at prestigious—and highly selective—Princeton University. Devastated when she’s suddenly dumped by her live-in partner (Michael Sheen), an English professor who’s gotten one of his departmental colleagues pregnant, she suffers a second blow when she’s persuaded to visit a an unorthodox private high school called New Quest on one of her recruitment trips by its charmingly scruffy owner John Pressman (Paul Rudd). While she’s there, he informs her that his best student—incredibly bright misfit Jeremiah (Nat Wolff), who was raised by middle-class foster parents and had bombed out at his previous school—is actually the son she gave up for adoption eighteen years earlier.

Portia does remarkably little research to confirm John’s allegation, instead becoming devoted to the idea of getting the boy accepted into Princeton despite his less than stellar academic record. To do that, she cultivates Connie (Gloria Reuben), her bitterest rival in the admissions staff, with whom she’s competing to succeed their boss (Wallace Shawn), and bends over backwards to compromise on candidates preferred by other counselors. But when those tactics prove insufficient, she’s willing to pervert the process—and put her job on the line—to secure one of the coveted slots for the kid.

There’s a crucial problem in the script that Karen Croner has adapted from Jean Hanff Korelitz’s novel. Portia and John—who are obviously fated to fall for each other despite her initial resistance (a scene with a pregnant cow that ends with them taking a side-by-side shower seems to reach back as far as “It Happened One Night” for inspiration)—are supposed to be smart people, but they act in remarkably foolish ways. She embarrasses herself while Jeremiah’s on a campus visit by disguising herself as a student to observe him at a dorm party—the sort of stuff Lucy Ricardo might have done. Her inability to deal intelligently with being jilted takes a series of slapstick turns that veer into stupidity when she encounters her old flame and his new squeeze—she wrecks her car gawking at them or (even worse) throws up on seeing them together. Frankly the part seems to have been fashioned for Fey’s brand of TV ditsiness rather than requiring something new from her; and the result is that the students meandering about the campus frankly seem more mature than Portia.

As for Rudd’s Jonathan, this is a character who’s supposed to be a Dartmouth grad with knowledge of the inner workings of academia, yet he goes out of his way to insult one of Jeremiah’s on-campus interviewers and act the smug rebel—though always with that patented Rudd smirk. And a subplot about Jonathan’s own parental problems—he has an adopted son he doesn’t exactly connect with—is all too obviously designed as a counterpoint to Portia’s impending motherhood, in a device with an overly literary feel.

There is some consolation in the work of the supporting cast. Wolff is ingratiating, if hardly charismatic, and Shawn earns a few smiles with his customary dyspeptic manner. Best of all is Lily Tomlin, who uses her grumpy persona to good effect as Portia’s free-spirited mother, even if her having to wield a shotgun at one point goes too far. There’s an amusing subplot about her involvement with an equally idiosyncratic Princeton philosophy professor, which suggests that a script about their relationship would have been preferable to the one we get here. Sheen, however, is about as subtle as Benny Hill.

“Admission” has been smoothly made, with fine cinematography by Declan Quinn and nice behind-the-camera contributions on all sides. Princeton doesn’t always come off especially well—a repeated joke about it coming in second in national rankings might be less funny than painful to the school—and one would like to know its official reaction to the picture, which it might not necessarily give a high grade. (Do they regret allowing the film to be shot on campus?) As for everybody else, at best the movie deserves to be relegated to your waiting list (at Netflicks, perhaps) rather than given a straight acceptance at the theatre.