There was an undeniable gleam in her eyes and an unerasable smile on her face. They betrayed how New York cabaret darling Nellie McKay was privately winking at the audience throughout her performance of "A Girl Named Bill" on Monday at the Dakota Jazz Club.

McKay's cabaret musical tells the true story of Billy Tipton, a jazz pianist/singer from the late 1930s until the 1970s who was discovered to be anatomically female during a 1989 autopsy in Spokane. There has been an opera, a play and an off-Broadway musical about Tipton; there's even a Seattle feminist band called the Billy Tipton Memorial Saxophone Quartet.

But there's nothing quite like McKay. She's not normal, which is a good thing, especially for tackling Tipton's life story. The abundantly talented 34-year-old is smart and smart-alecky, clever and creative, fast and fearless, proudly unhip and gleefully old-fashioned. She likes to challenge herself and her audience. And that's what she's doing with "A Girl Named Bill."

In these Caitlyn Jenner times, this musical about gender fluidity could provide profound commentary and wide resonance. However, by sticking to song and dialogue, McKay doesn't make Tipton's story clear enough. The entertaining 75-minute musical begs for narration so the audience can connect the dots. And hyperactive McKay could slow down a tad so the jokes and emotions can settle in.

Sometimes the little skits make things clear, such as when Dorothy Tipton (Billy's birth name), in a dowdy flour-sack dress, goes looking for jazz gigs and gets turned away. Other times, the show takes great leaps, such as when Billy is suddenly helping his two young sons in the bathtub. OK, we kinda knew Billy was married, but where did the sons come from? (Answer: They were adopted. He actually had three sons and five wives, but this show doesn't communicate that.)

When it comes to the music, "A Girl Named Bill" succeeds. McKay has an outstanding ear for period pieces, many of whose lyrics — such as "Jazz Up Your Lingerie," Jelly Roll Morton's sexually explicit "Winin' Boy Blues" and "A Hymn to Him (Why Can't a Woman Be More Like a Man)" from "My Fair Lady" — further the story lines.

McKay contributes a few originals, including the vaudevillian ditty "I'm in the Luckiest Mood" and "Please Park Here I'm Lonely," which is featured during a silly skit with her musicians. Her three players offer a few songs, such as a lite version of Cream's heavy rocker "Blue Condition," while she's offstage changing from one oversized dinner jacket to another. All of them seem to be four sizes too big because McKay can't resist shtick and corn. Witness some of Billy's jokes such as "there are three sexes — male sex, female sex, and insects."

Like Tipton, McKay can't resist doing impressions of Jimmy Durante, Elvis Presley, Liberace and Bob Dylan, including miming a guitar solo on ukulele. And she plays a mean piano in a variety of styles. That's no impression. That's the super-skillful McKay.

Her true colors were re­vealed Monday during an encore of Loretta Lynn's 1971 classic "One's on the Way," which McKay dedicated to Planned Parenthood. The song is often seen as a cry of frustration for staying home and raising kids. Ardent feminist McKay ended it with a typical twist by yanking off her short Billy Tipton wig and tossing it into the Minneapolis air a la Mary Tyler Moore.

Twitter: @JonBream • 612-673-1719