It’s hard to name two more likable actors than Tina Fey and Paul Rudd. They’re charming, smart and hilarious. They’re comfortable sticking to a script or wildly improvising.

So why is their new dramedy so clunky?

“Admission” probably began with a clear artistic vision but was compromised along the way. The messy result offers glimpses of greatness dragged down by scenes that are bafflingly tone-deaf.

Fey plays Portia Nathan, an admissions officer at Princeton University. Portia takes her job uber-seriously, knowing that she controls the fate of thousands of applicants hoping to attend the most prestigious university in the country. Well, second-most, anyway. The revelation the school has slipped to No. 2 in the U.S. News and World Report rankings rankles her boss (Wallace Shawn). He ups the pressure on his staff to go after students who really matter: those who can change the world.

So she agrees to visit an alternative high school run by John Pressman (Rudd, who was raised in Overland Park and attended KU). It’s a place that teaches hands-on courses about Third World development, populated by students who dismiss “elitist institutions” such as Princeton. All except one student, Jeremiah (Nat Wolff), who is dying to attend.

John believes him to be the eccentric prodigy Princeton should pursue. But the teacher’s push for Jeremiah stems not only from admiration but a buried secret that could compromise Portia’s career principles.

“Admission” enjoys exploring how children do all they can to avoid ending up like their parents. John has an adopted African son, Nelson (Travaris Spears), who yearns to stop globetrotting. He thinks Portia is fascinating because, “You’re a normal, boring adult.” When his dad begins romancing Portia, Nelson hopes the family will stay put for a change.

Similarly, the uptight, methodical Portia is the product of radical single mom Susannah (Lily Tomlin). Brandishing a Bella Abzug tattoo and an acid tongue, she’s authored such books as “The Masculine Myth.” Her idea of a mother-daughter talk involves blindsiding Portia with an oh-by-the-way mention that she recently endured a double mastectomy.

Susannah remains upset that her only child has wasted her life working for The Man. “You were born an Amazon,” she scolds Portia. Veteran Tomlin delivers the film’s most significant performance, adding layers of poignant subtext to a character who might have turned gimmicky.

The individuals introduced by screenwriter Karen Croner (based on the novel by Jean Hanff Korelitz) are intriguing, yet the plot often foists them into the trappings of light romantic comedies. Awkward misunderstandings, contrived revelations, co-worker rivalries, ex-boyfriend humiliations — all these elements mingle to the strains of a perky-but-inoffensive soundtrack. (Even Fey’s iconic facial scar is airbrushed out of the film’s promo poster.)

Director Paul Weitz (“In Good Company”) provides a few visual gags that stick. As Portia contemplates resumes, the prospective students fancifully appear in her office, flaunting the attributes they think will get them into Princeton. (One gymnastics champion does handstands on a desk while boasting, “My grandfather is Cuban …. and in a wheelchair!”)

When these applicants get rejected, they plummet through a trapdoor. Yet Weitz stages an equal amount of flat and occasionally embarrassing ones (cow birthing, anyone?).

Admirably, “Admission” makes some bold moves. It often places these likable actors in unlikable situations, where their behavior proves morally dubious. This welcome dramatic weight almost redeems the film, offsetting the drought of romantic sparks and humor.