During the New York Gilbert & Sullivan Players’ short City Center season, which runs through January 15, each performance will begin in the same way. A bald man will pop up from the orchestra pit like a jack-in-the-box, turn to the crowd, and wave his arms enthusiastically, to hearty applause. If this man seems part conductor and part cheerleader, it’s not far from the truth, for Albert Bergeret is something of an old-fashioned local impresario. He has been conducting the overtures, managing the stage direction, and designing and building the sets for the Gilbert & Sullivan Players for more than 30 years. (His wife, Gail Wofford, makes the costumes.) All this gives the productions a mom-and-pop-shop feeling; they have New York talent, but with the warmth of community theater.

That’s all to the good, since it’s a help to have the audience firmly on your side when mounting two tricky operettas like “H.M.S. Pinafore” and “The Mikado.” Besides the tongue-tripping lyrics, there are pressing dramaturgical problems – dated references, overextended jokes, the occasional leaden character. Most difficult of all is the task of adapting “The Mikado” – a blatantly stereotyped piece that has frequently been called racist – for a contemporary audience.

Mr. Bergeret and his ensemble succeed on most counts. The seasoned principals carry the main roles with aplomb. Stephen O’Brien makes a marvelous Sir Joseph Porter in “Pinafore”; his crystal-clear enunciation of the patter songs is a delight, and his delivery of the classic “When I Was a Lad” has everything you want from a Gilbert and Sullivan number: insouciance, biting wit, and belly laughs. Angela Smith has a nice way with Buttercup’s lines and lyrics. Laurelyn Watson, a clear-as-a-bell soprano, gives Yum-Yum a kind of unassuming dignity that might seem impossible given the character’s name. When you hear singers like these, you wish that every member of the cast could articulate the words so incisively; at times, certain singers (and certain acoustics) produce some ear strain.

Still, the jaunty live orchestra puts a spring in the chorus’s step, and the dance numbers zip along nicely. Mr. Bergeret’s staging is clever – he manages the pratfalls and stage business (fat man who can’t roll over his own stomach, man dragging an oversized cleaver) in the spirit of the dining hall revel. His general ease with creating good, serviceable stage pictures is so pleasing that it was perplexing to see him occasionally get too clever (milking the crowd for applause) or too sentimental (love ballads that were more opera-like than operetta-like). Nevertheless, between Mr. Bergeret’s lively baton and his good comic timing, the shows sail briskly ahead.

Mr. Bergeret’s sets and Ms. Wofford’s costumes simultaneously render each space a world apart from dear Old England and a product of Gilbert and Sullivan’s imaginations. Their man o’ war ship is pure English fantasy, its colors muted as if bleached by a blazing sun, its decks and masts and middy blouses neat as a pin. The “Mikado” set is a riot of Japaniana, as if every last item a Victorian knew were crammed into its frame – a shrine gate, an arched bridge over a pond, rice paper screens, and a mural reminiscent of Hiroshige’s paintings of Edo, replete with cherry blossoms and mountains. Here again, the costumes suggest a dated British notion of a storybook Japan: kimonos and sandals, rice paddy hats, and black wigs (some with Chinese ponytails), and slanting eye makeup.

Despite some significant rewrites to bring it into the 21st century, “The Mikado” remains, for this critic, an uncomfortable evening. One can argue that Gilbert and Sullivan are equal-opportunity lampooners, that their England is as warped and caricatured as their Japan, yet the discomfort remains during the “tee-hee-hee” schoolgirl bits and especially during “Mi-Ya Sa-Ma,” a collection of syllables that Mr. Bergeret’s troupe turns into a litany of Mitsubishi, Toyota, and Sony. This production follows a long-fashionable trend of updating Gilbert and Sullivan lyrics, inserting new names on the list of those who would not be missed, and so on. The City Center crowd certainly enjoyed the new jokes about cell phones, homeland security, and Paris Hilton, but these seem rather obvious targets in comparison with the sly turns of phrase W.S. Gilbert favored.

The New York Gilbert & Sullivan Players are the city’s custodians of a tradition of delightful running notes, quick-witted rhymes, and absurd plots layered with irony and a bit of melodrama. They succeed in animating a classic repertoire for a new generation, but have yet to solve the problem of how to throw out the old bathwater while protecting the bouncing baby. Perhaps that task is impossible, but if it can be done, it’s probably by that multitalented man in the pit.

Until January 15 (130 W. 55th Street, between Sixth and Seventh Avenues, 212-581-1212).