The main resulting innovation is a new prologue, written by Mr. Auxier, which frames the operetta as the fantasy of a Victorian librettist, caused by mild head trauma. The scene is the London office of the D’Oyly Carte Opera Company in 1884, where Gilbert (Joshua Miller) and Sullivan (David Macaluso) have just unveiled their latest show, “Princess Ida.” As actors interrupt with petitions and complaints, the company’s impresario, Richard D’Oyly Carte (Matthew Wages), urges the two men to conceive their next joint venture.

As it happens, an exhibition of Japanese art and handicrafts is being set up in town, and D’Oyly Carte has brought a selection for Gilbert and Sullivan to preview. Amid the chatter, nonsense syllables pop out that will coalesce into the made-up Japanese names of “The Mikado”: A soprano’s delectable voice is deemed “yum-yummy indeed”; a vexatious but talented tenor is “that ill-mannered, unwashed, nincum — nanki — oh, poo!” When Gilbert is struck on the head by a falling object, the stage is set for an operetta in which a prince disguised as the minstrel Nanki-Poo (the very accomplished tenor Daniel Greenwood) vies for the hand of the lovely Yum-Yum (the pert soprano Sarah Caldwell Smith).

The prologue is not just an effective way to frame the show and cushion the impact of its more offensive elements. It also feels quite organic. After all, Gilbert & Sullivan operettas draw much of their comedy from overt references to their own artifice. Jokes about tenors or recitatives, for instance, playfully turn the spotlight on the conventions of the genre. Sometimes the story, in all its magnificent ridiculousness, seems like mere scaffolding, propping up the ritual of the performance.

This sense is reinforced by the imaginative costumes by Quinto Ott, which mix Victorian silhouettes with vibrant Asian fabrics. The actors who play Gilbert, Sullivan and D’Oyly Carte in the prologue remain recognizably British as they take on the roles of Pish-Tush, Ko-Ko and Poo-Bah. Add to that the checkered ethnic makeup of the chorus, and the Japanese setting becomes unobtrusive to the point of invisibility.

What’s left is a tightly choreographed comedy of manners with coolly precise slapstick and the requisite helping of improvised winks at the New York audience. Spoken dialogue flows smoothly into patter arias and ensemble numbers, some of them sung with a weightless, silky blend that would be the envy of more classically rooted choirs. The orchestra, led by Aaron Gandy, struggles to measure up much of the time, but that irritation, too, recedes into the distance as the madcap merriment takes its course.