ONE OF the commonly cited ills of the commercial theater these days is a shortage of strong producers and directors -- people with the discernment to see what's wrong with a show and the grumption to set things right. So the saga of "Sophisticated Ladies," the Duke Ellington revue that left the Kennedy Center last weekend bound for Broadway, could be welcome news for the theater in general, not only for the people whose careers and pocketbooks hang in the balance.

When "Sophisticated Ladies" arrived here from Philadelphia, it came well-attended by rumors, all of them bad. The reviews had been alarming. The show was said to be much too long. The musical numbers were interspersed with narration that pleased no one. The sets were so cumbersome that extricating them from the Forrest Theater in Philadelphia and installing them at the Opera House caused a two-day postponement of the show's Washington opening.

But once the company had arrived here, these problems were forgotten in a flurry of backstage developments apparently lifted from the plot of "42nd Street" or some Mickey Rooney-Judy Garland show-business movie. "Sophisticated Ladies" had opened on a Tuesday night. On Wednesday morning, the producers announced the resignation of their star, Gregory Hines, who had generally been hailed as the show's greatest single asset.

The producers said Hines' understudy, Gregg Burge, would assume the role as of the Wednesday matinee. That never happened. The matinee was canceled, an eager audience sent home and the cancellation attributed by a spokesman to Burge's need for more preparation time. But the official story began dissolving, Watergate-style, Wednesday afternoon. Hines was suddenly back in the show, and we were told he had not resigned in any case -- he had been fired. Or, as a second official announcement had it, he had never really left the show at all.

The truth, emerging in its own good time, was that Hines had been fired for disputing director-choreographer Donald McKayle's authority, and for going over McKayle's head with suggestions for fixing the show. "I was very aggressive, maybe too aggressive," the star later explained. The producers, with traditional employerly generosity, had described his departure as a resignation; but Hines, in a refreshing reversal of tradition, had wanted it known he had been fired -- he didn't want to be thought a quitter.

Shortly before curtain-time for the Wednesday matinee, the rest of the cast had learned about his firing, and they had promptly refused to perform. In a heart-to-heart talk with the producers, Hines' fellow actors, singers and dancers had suggested that if McKayle and Hines couldn't work together, perhaps McKayle rather than Hines should make away. And the producers had been persuaded.

"This company is one of the warmest, tightest companies I've ever been involved with," said Hines. "We're on the same team now," said co-producer Roger Berlind. "We're working together and we're going to stay together." McKayle, who had been not only the show's director and choreographer but also its creator, checked out of his hotel without comment.

"Sophisticated Ladies" was (and remains) a big production, with 16 performers, a 20-piece band, innumerable costumes and a complex interplay of neon lights, backdrops, foredrops and moving platforms. In the version of the show that opened here Jan. 13, the majesty of Duke Ellington's music tended to get lost in all that bigness, and with the subsequent personnel fracases, with time and presumably money running out, and with Inaugural distractions that dampened business and stalled the search for a new director, the ingredients of a major, rip-roaring pre-Broadway disaster seemed to be present. Memories of "Carmelina" and "Swing" danced in the Kennedy Center air.

And then, miraculously, "Sophisticated Ladies" began to find itself. It wasn't a miracle, of course.It was old-fashioned professional smarts, hard work and vast talent -- talent that had been part of "Sophisticated Ladies" from the beginning, if not always the most prominent part. During the last two weeks of the show's run here, after Michael Smuin of the San Francisco Ballet had been signed to take over McKayle's duties, thousands of people saw "Sophisticated Ladies," and the show they saw was changing from night to night. Numbers were dropped, inserted and rearranged, choreography was removed, narration and dialogue were rewritten and stripped down, and as soon as the cast got used to one of these changes, another loomed to put them off stride.

But they were very much on stride at the final Sunday matinee, and the changes had yielded a show that was livelier, much lighter on its feet, much more satisfying, and still awaiting further refinements.

Among the most visible changes: a new opening with dancers Gregg Burge and Hinton Battle singing and dancing "I've Got to Be a Rug Cutter"; a faster tempo throughout; friskier orchestrations and musicianship; a more thorough blending of the band into the show, with a saxophonist brought forward to accompany Hines and Phyllis Hyman in "Take the 'A' Train," and Hines moving into the band (playing drums) for "Diminuendo use of Judith Jamison's dancing and Priscilla Baskerville's singing, with the two given exlusive and felicitous custody over "In My Solitude," and snappier, more focused choreography throughout.

Several substantial numbers -- including the "Kentucky Club" sequence, "Black and Tan Fantasy," "King of the Magi" and "Black Beauty" -- had been dropped outright. So had a grotesque little joke (covering a scene change) about a child mistaken for a monkey. And so had Hines' elaborate narration about his (and the Duke's) search for "the perfect note." Now the narration consisted of little beyond Hines' invitation to the audience to "step into Duke's world," and the invitation had become a far more enticing one as a result.

After the move to New York last week, the show took the further gamble of postponing its opening and canceling several previews to accommodate a solid week of rehearsals and yet more changes. Anything can happen when "Sophisticated Ladies" opens on Broadway (March 1, Lunt-Fontanne Theater), but the show left Washington looking very good indeed. In an age of declining investment, the sponsors of "Sophisticated Ladies" could have cut and run. Instead, they're off and running.