Once Upon a Mattress exists under the longest of long shadows. The lead role of Princess Winnifred was, in 1959, the breakthrough for Carol Burnett, and who on earth wants to invite comparison to her? Although the show is staged all the time at the drama-club level — because it’s funny and goofy, colorful and slapsticky, with a fairy-tale story and a solid number of parts to distribute among the 11th-graders — it’s not so often produced in big, professional settings. That may also be because, the frothiness of the story notwithstanding, Winnifred is actually a pretty tough role to handle.

The show’s composer, Mary Rodgers, in the wonderful memoir she co-wrote with Jesse Green, had this to say: It’s a very hard part to cast. You need a real clown with a great voice, someone with a huge personality but immediately likable, and there aren’t many performers like that. Only once since the original production has it come to Broadway, with Sarah Jessica Parker in 1996, and she wasn’t quite right for it.

Burnett would belt and honk and sling herself around the stage, playing Winnifred too loud and too broad and therefore exactly right; Parker, regardless of her comedy skills, is not the same kind of physically robust, almost circusy performer, and that revealed the show’s weaknesses. And those weaknesses are real: It’s silly, with a 1950s battle-of-the-sexes cheekiness, which is fun but maybe not 150 minutes’ worth of fun, and a mother-and-son plot that I suspec.