But Seriously, Folks . . . : Rhino Records has a problem. The funky, irreverent company faces respectability as it tries to succeed big-time and not sell out.

Is Rhino Records concerned?

Do Milli Vanilli hold their tongues and move their lips?

A startling thing has happened to Rhino, the Santa Monica-based label that has been called the Mad magazine of the music industry. Feisty, funky, irreverent Rhino is facing-- no, no, it’s too hideous-- respectability.

Can it be true?

Did Rhino earn its first three Grammy nominations this year?

How did this happen to a company whose logo is a salacious-looking rhino, who sometimes appears in a black-leather jacket a la young Marlon Brando in “The Wild Ones.” (That’s the movie in which Brando’s biker is asked what he is rebelling against, and he sneers back, “Whatcha got?”)

What has become of the label that once boldly issued the collected musical oeuvre of God’s gift to peanut butter, Annette Funicello, including the never-to-be-forgotten “Tall Paul,” on a picture disc? What has happened to the wonderful folks whose first chart-buster--in 1978--was a cover version of Led Zeppelin’s “Whole Lotta Love” performed by the Temple City Kazoo Orchestra?

What’s happened, in the course of a dozen years in the music business, is that Rhino has established a solid reputation for producing top quality reissues and brilliantly packaged oddities, including a “Teenage Tragedy” compilation that comes with tissues in case “Leader of the Pack” reduces you to tears. And it is now in the process of creating a future solidly grounded in the unpredictable, which always has been its forte.

Rhino has built a $33-million-a-year business by appealing to strange musical passions--man’s previously unrecognized need for the 10 best versions of “Louie, Louie,” for instance. But because the people at Rhino are smart as well as unorthodox, and fuss over such details as exquisite sound, they have found a niche--and a dilemma. How do you succeed without selling out? How do you grow and stay the same?

Rhino is trying. Take the Grammys, please. Rhino has a reputation to protect, and it has nothing to do with acceptance speeches and evening dress. So, it did not engage in saturation-bombing the media with self-serving press releases about its Jack Kerouac collection, nominated for best historical recording and liner notes, and “Comic Relief ‘90,” nominated for best comedy album. Instead, Rhino came up with something more its style: the Rhino Awards.

Handed out Feb. 19--the day before the Grammys--over bagels at Canter’s delicatessen, the Rhinos consisted of the critics’ picks of the worst the music business had to offer last year. The brainchild of Harold Bronson, Rhino’s co-founder and managing director, the awards tweaked the recording industry and its machine-made stars.

The awards, Bronson says, were a return to the irreverent, satirical Rhino of its origins. “As time goes by, it becomes more difficult to express that side,” Bronson allowed.

And so Vanilla Ice was the big “winner,” whose three Rhinos included the LeRoy Neiman Award for worst artist.

But it was Madonna whose “Justify My Love” captured the dreaded Carl “Kung Fu Fighting” Douglas Award for most inferior single.

“I even got a call from the lawyer for the publisher of that song,” says Bronson.

Bronson, 40, doesn’t smile when he says it, but he somehow brings to mind a schoolboy who has just got off a really great spitball.

In the beginning was the goof.

Rhino, the label, grew out of Rhino, the Westwood Boulevard record store, founded in 1973 by former social worker Richard Foos, now 41. Rhino, the legend, was born when Foos and store manager Bronson (who once sang with a group called Mogen David and the Winos) began to apply their manic creativity to the retail record business. They would give a nickel to anyone who took home an album by red-headed Danny Bonaduce of “The Partridge Family” and promised to listen to it. They had puckish theme days: Idi Amin’s birthday and Jewish Day, when customers were invited to bargain hard with the sales staff and were offerred a free yarmulke. On Thanksgiving they sold their “turkey albums” for 40 cents a pound.

In 1978 they cut their first record, “Go to Rhino Records,” which was a plug for the store ad-libbed by pioneer street person Wild Man Fischer. It was given away free to customers, perhaps because the Rhino Brothers, as they had begun calling themselves, knew nobody would buy it.

That year, Foos sold the store, and a very strange record company was born.

It’s easy to stereotype Rhino as the label that thoughtfully provided an air-sickness bag with its collection of the World’s Worst Records. Rhino staffers try to correct that all-yuks-all-the-time image without sounding too pretentious.

“We’re not a one-dimensional label,” explains James Austin, associate director for artists and repertoire. Indeed the label has surprising range. It has produced definitive collections of surf and guitar music and documented pop music’s British Invasion. It sells music by everyone from Nat King Cole to Carl Perkins. It also recently started a sister label, RNA, which features new artists, including such not-yet-household names as Exene Cervenka, Steve Wynn, and the team of Peter Holsapple and Chris Stamey.

“The impetus for projects always comes from something that someone in the company is passionate about,” says Gary Stewart, vice president for artists and repertoire. In an organization as committedly egalitarian as Rhino, ideas can come from almost anywhere. Two guys in the shipping department used to try to one-up each other by finding truly appalling versions of songs to play at work. The result was “Golden Throats: The Great Celebrity Sing-Off,” which features Jack Webb crooning “Try a Little Tenderness” and Leonard Nimoy belting out “Proud Mary.”

Austin’s babies have included the Jack Kerouac collection, the label’s most prestigious project so far. The record set includes the complete recorded works of the giant of the Beat Generation and functions as a Kerouac archive in a box.

Whatever Rhino does, it does with the music fanatic in mind. Sound quality is an obsession with the staff. “Usually you’re doing it for posterity,” says Stewart, “and it’s your last chance to get it right.”

Rhino holds something it calls its More Brains Meeting, a weekly strategy session, on Friday mornings. A dozen key staffers (there are more than 90 employees) sit around a conference table and talk about current and future projects. The Diet Pepsi flows.

Bronson says that he and his partner want Rhino to be profitable, but they also want it to be a place where creative people want to go to work in the morning. And they want Rhino to be socially responsible as well. Like such corporate soulmates as Ben & Jerry’s, the politically correct ice-cream people, the Rhino management wants to sell its product but keep its planet. The back of the Rhino catalogue, which looks like a comic book, includes a list of things customers can do to save the Earth. Staffers get time off to do community service. Needless to say, there is no dress code.

One of the ways Rhino preserves its identity as a talented maverick, Bronson says, is by hiring people “minimally tarnished” by involvement with the record industry.

“Quite often people who have spent time at major labels pick up a lot of bad habits,” he says. Pressed to specify those defects, he cites a tendency to overspend and a lack of creativity.

At a recent Friday morning meeting, Gary Stewart is making the case for one of his weirder projects. It is pure, unadulterated Rhino.

“Who hates B. J. Thomas the most?” he asks his colleagues, all of whom instantly raise their hands. Stewart has just passed out cassettes of the new “Best of B. J. Thomas” album.

It is hard to imagine another record company that would gamble its own money on the world’s willingness to invest in the greatest hits of the faded star who sang “Raindrops Keep Fallin’ on My Head.”

“A lot of people think of this guy as a pretty square artist,” Stewart continues. Prompted by the same interior imp, the staffers begin snapping their fingers in unison and singing another of Thomas’ biggies: “Hey, won’t you play another somebody-done-somebody-wrong song?”

Everyone laughs.

Stewart laughs, too, but is undeterred.

“I’m gonna stand tall here,” he says, winding up to defend yet another record that only a Rhino could love.