Ask Future Islands: When you can get a real reaction out of David Letterman, a jaded and sarcastic old motherfucker who’s seen everything, that’s something you can hang your hat on. Whatever happens for the rest of their careers, the members of Foxygen can say that they did that. Last night, the L.A. psych-poppers made their TV debut on Letterman, playing “How Can You Really,” the first single from their 2014 double album …And Star Power. They seized that moment for everything it was worth. They brought a huge backing band, including an energetically choreographed trio of backup singers, and they played with all the spazzy, erratic glam-rock energy they could summon. It was quite a sight. Letterman loved it: “That’s all we’re looking for, for god’s sakes! No more phone calls! We have a winner, ladies and gentlemen!” Watch it all happen below.

…And Star Power is out now on Jagjaguwar.