Joe Russo was totally stressed when he walked off an Oakland, Calif., stage at set break during the 2009 debut of Furthur, a group built around the former Grateful Dead members Bob Weir and Phil Lesh. Unversed in the Dead’s massive repertoire only weeks earlier, Mr. Russo, a Brooklyn drummer, was relying heavily on a laptop for assistance in front of an audience for whom the material was uncut cultural DNA. Spotting Mr. Weir backstage, he apologized for his high anxiety and requested advice. His new boss obliged: “Maybe take some mushrooms?”

While he didn’t follow the prescription, “All the tension fell out of my body and I knew nobody would die if I screwed up,” Mr. Russo recalled recently. “It was a very free place.”

And things have only gotten freer since. Sitting in the sunny backyard of the Park Slope apartment he shares with his wife and 2-year-old daughter, the amiable shaggy dog of a musician reflected upon Joe Russo’s Almost Dead, the unexpectedly successful powerhouse of a Grateful Dead tribute band he leads. (The group performs Thursday in Prospect Park as part of BRIC’s Celebrate Brooklyn! Festival.)

JRAD, as the quintet is more casually known, is a vehicle for Mr. Russo and four musical friends of at least 20 years — the keyboardist Marco Benevento, the bassist Dave Dreiwitz, and the guitarists (and main vocalists) Tom Hamilton and Scott Metzger — to improvise extravagantly around the Dead’s emotionally sublime and often quirky songwriting. They eschew the laid-back fidelity of both official offshoots like Dead & Company (which includes three of the so-called “core four” surviving band members) and other tribute acts like the Dark Star Orchestra. Think instead of the Dead on a gleeful amphetamine drip.