Dana Carvey has a long comedy history with Johnny Carson, from wowing the host on early Tonight Show appearances to angering him with that Carsenio character on Saturday Night Live, an impression that made Carson seem old and out-of-touch. Decades later, Carvey still does Carson in his act, including a running bit about the late-night host getting pulled over for drunk driving.

While Carson had real-life DUIs, the gag is mostly a goof on old-timey drink names and inane cocktail bars: “Sorry, Officer, I had a Strawberry Boom Boom at the Winking Rat.” Or: “I had a Feisty Feather at Slippery Tim’s.” Carvey is still improvising variations on the joke, he told David Spade on their Superfly podcast this week, revealing which improvised version killed the hardest at a recent appearance: “I had a Double Leaky Giraffe at the Desperate Sponge.”

Carvey goofing on Carson’s under-the-influence excuses sparked...