When your father is the greatest composer in the history of musical theater, charting your own course in that field can take some pluck. Richard Rodgers’s elder daughter, who was also an author and screenwriter, had that quality in spades, as is known by anyone who’s read “Shy: The Alarmingly Outspoken Memoirs of Mary Rodgers.”

The younger Rodgers contributed to several musicals, and her best was her first: “Once Upon A Mattress,” a witty and charming takeoff on Hans Christian Anderson’s “The Princess and the Pea,” with lyrics by another creative multi-tasker, Marshall Barer, and a book by Barer, Dean Fuller, and Jay Thompson. The original Broadway production, which opened in 1959, starred a young Carol Burnett as Princess Winnifred, a heroine whose audacity and vivacity might have suggested Rodgers’s own, but cubed for comic effect.

In Lear deBessonet’s high-spirited and frequently hilarious new concert production of “Mattress” — being presented as part of the New York City Center Encores! series, for which Ms. deBessonet serves as artistic director — the role of Winnifred falls to one of today’s Broadway stars, Sutton Foster. While Ms. Foster’s undeniably impressive mix of singing, dancing, comedic chops, and sheer likeability have earned her a pair of Tony Awards and legions of fans, I’ll admit I’ve found her seemingly turbo-charged vibrancy — imagine if Mary Tyler Moore had, in her prime, been prescribed Adderall — overwhelming at times. 

Winnifred, happily, is a part that Ms. Foster was born to play; and in Ms. deBessonet, who as part of the series also helmed the luminous staging of “Into the Woods” that transferred to Broadway two years ago, the actress and her colleagues here have a shrewd and loving guide. Like the director’s “Woods,” her “Mattress” boasts a bevy of high-profile talent: Michael Urie, fresh off his stint in an uproarious new production of “Spamalot,” turns up as Prince Dauntless, who prior to Winnifred’s arrival at his castle is forced to sulk and cower as his domineering mother rejects one potential bride after another.

Harriet Harris is just as ideally cast as that imperious queen, who alternately coddles and harasses her son while the king, rendered mute by a spell but delightfully animated in David Patrick Kelly’s performance, looks on helplessly. Nikki Renée Daniels and Cheyenne Jackson sing beautifully as palace rose Lady Larken and her brawny but dimwitted beau, Sir Harry, and the Tony-winning “Some Like It Hot” star, J. Harrison Ghee, brings diva-worthy flamboyance — if not enough impish wit — to the role of the court jester.

Yet it’s Ms. Foster who truly carries the show, albeit with adorable assistance from Mr. Urie in their scenes together. All of this leading lady’s leading assets are on display here, from her sometimes underused capacity for dry, sly humor to that Energizer Bunny-like exuberance. The latter fuels rollicking and very funny production numbers, starting with a show-stopping “Shy” — performed upon Winnifred’s entrance after swimming a moat, as she’s still pulling leeches and other small animals from her body and hair.

Those creatures are new to “Mattress,” and Amy Sherman-Palladino’s concert adaptation adds other winking touches to the book, without messing with the medieval setting and vibe. Rodgers’s score remains consistently appealing, from the jaunty overture on; the songs here are certainly much more hummable than those her son, the celebrated composer and lyricist Adam Guettel, wrote for his latest, much darker work, an adaptation of “Days of Wine and Roses” that opens on Broadway this weekend.

Andrea Hood’s whimsical, pastel-heavy costumes perk up David Zinn’s predictably minimal set, though it’s likely the scenic design would be fleshed out were this “Mattress” to follow “Into the Woods” to Broadway. Whether that happens will depend, I’m sure, on the availability of Ms. Foster, who’s slated to soon step into the revival of “Sweeney Todd” now in production there; if she does, I would join her admirers in considering that a happy ending.