On April 28, Rae Sremmurd are in New York for their second appearance on The Tonight Show, where they’ll perform “Look Alive,” a single from their upcoming album. In the green room ahead of the taping, Swae Lee, 23 years old and the younger of the group’s two members, is camped in front of a mirror. He fixes his gaze on himself as he angles his face from side to side and plays with his hair — undershaved dreads, which he can wear draped over his eyes, twisted back in pigtail braids, or in a pineapple-like topknot.

“Gucci jackets!” his older brother, Jxmmi, 24, yelps from across the small room. Both boys are wearing brand new ones: Swae’s is embroidered with flowers, and Jxmmi’s, which he’s wearing over a bare chest, is a patchwork of shiny red, black, and green panels. “Do you know what truck nuts are?” he asks his half-dozen friends in the room, referencing the toy testicles that are attached under the rear bumper of pickup trucks. He wants some.

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The taping starts and the guys watch on a monitor in the green room. During his monologue, host Jimmy Fallon drapes his suit jacket over his shoulders like a cape, and dances to a song by Styx. “He gotta be so high,” Jxmmi says. “I wonder if he smokes weed.” Fallon keeps the gag going as the show continues: he does “cape time” with first guest Adam Levine, the singer, and second guest Michael Shannon, the actor. “We gotta do the capes,” says JJ, Rae Sremmurd’s DJ, who goes by D_JaySremm.

The room, used for musical guests, is stocked with instruments to play with. JJ picks up a banjo and plucks out a riff, while Swae freestyles a melody and raps. Later, they sit together at a piano, JJ plinking keys on the upper octaves while Swae harmonizes on the lower end.

Someone pops in to announce their turn has come, and the boys walk ahead to the stage. Trailing behind them in the hallway, I hear an employee of The Tonight Show say: “I’m worried about this one.”

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A slight like this doesn’t come as a total surprise. Rae Sremmurd’s music is celebrated for its feel-good energy, but it has also been derided as superficial, or written off as novelty in the cartoonish tradition of Kriss Kross. The brothers have jumped around at photoshoots, ridden skateboards through midtown offices, and figured out a way to combine Auto-Tune with their voices to sound even younger than they are. At a time when many acclaimed rappers are expressing pain, or anger, or political turmoil, they have been distinguished above all by a sense of joy. Their music’s approachability and pop appeal has made them a fixture on radio nationwide, in clubs, and on college campuses. But by some, their exuberance has been taken for weakness.