Alvin Ailey American Dance Theater’s Jacquelin Harris and Megan Jakel in Robert Battle's “Ella.” (Teresa Wood)

Pity Ella Fitzgerald’s sidemen, keeping up with a voice that could soar, skim and leap like some kind of winged creature. Only the most predatory reflexes could contend with her improvisations.

The killer instinct: Surely that’s what drove the dancers in “Ella,” a tribute to the jazz singer. It was the shortest but most powerful work on the Alvin Ailey American Dance Theater program at the Kennedy Center Opera House on Tuesday night.

Fitzgerald’s vocal licks met their match in the two women’s twists, jumps and rubbery bounces. The concept was crazy — dancing to Fitzgerald’s stunning scat solo in her recording of “Airmail Special,” which needs no other accessory. But Ailey’s Artistic Director Robert Battle, who choreographed “Ella” in 2008, is just that kind of crazy, and ambitious. And smart.

“Ella” is a play of contrasts, and a fiery tribute to female power, which feels very au courant. There’s Fitzgerald on the one hand, freely diddle-ee-dopping while maintaining total musical control. And the dancers, reacting explosively with the same virtuosic precision amid a rhythmic storm. A solo dance might have been impressive, but not nearly as risky. Battle ups the ante with two women moving as one, hammering out a new move for every scat syllable with perfect synchrony. Dancers Jacquelin Harris and Megan Jakel didn’t have the luxury of improvisation; this was a finely drilled display, and the mind reels imagining the rehearsals leading up to it. 

Just as Fitzgerald abandoned intelligible lyrics, the dancers abandoned physical limits. They spun, leapt, collapsed, sprang up and slung themselves around like ink in the hand of a mad doodler. When a line of men slumped sheepishly along the back wall at one point, everyone got the joke; who could compete with these three women, the two dancers and Fitzgerald? “Ella” was a delightful tribute to a great artist in her centennial year. I hope the dancers had an ice bath waiting for them backstage.

Alvin Ailey American Dance Theater in Johan Inger’s “Walking Mad.” (Teresa Wood)

The Ailey dancers look best in such a restive, sophisticated challenge. They had another one in “Walking Mad,” a new work by Swedish choreographer Johan Inger. Of all the dances I’ve seen inspired by the hypnotic crescendo of Ravel’s “Bolero,” this is the most interesting. Like “Ella,” it exhausted the possibilities. It used familiar music in a new way, exploring just about everything that could be done with a movable wooden wall and nine dancers. Inger led Stockholm’s Cullberg Ballet for five years, and “Walking Mad” was infused with the stark, unsettling and quirkily theatrical style of that experimental company founded by the acclaimed choreographer Birgit Cullberg. 

Were the men flirting with the woman they discovered huddled alone in a shadowed corner of the stage? Or — as they tossed her higher and more roughly from man to man — were they assaulting her? Images of affection quickly and subtly turned ambiguous. Clever humor took a dark turn. I’m eager to see more from Inger.

It’s also Dizzy Gillespie’s centennial, and the Ailey dancers unfurled a tribute for him as well, in a brushed-up production of Billy Wilson’s 1992 “The Winter in Lisbon,” with music by Gillespie and Charles Fishman, founder of the DC Jazz Festival. Like “Revelations,” the perennial Ailey finale, this piece showed the showbiz side of Ailey, polished to a high gloss. But there’s more of a pulse in the works with edge.

Alvin Ailey American Dance Theater performs mixed-repertory programs at the Kennedy Center Opera House through Sunday. kennedy-center.org.