1. PAUL SHAFFER
The colorful Canadian bandleader was really two sidekicks in one: an Ed McMahon–Doc Severinsen hybrid with the talent to back up A-list guest musicians and the ability to banter with Dave as an equal. Perhaps more essentially, Shaffer served as the simple syrup to Letterman’s bitters, undercutting the host’s grumpiness with wacky irreverence.
2. LARRY “BUD” MELMAN
A celebration of oddness, actor Calvert DeForest was an awkward, unassuming Truman Capote look- and soundalike who came off like a stranger trying to befriend you on a bus–the guy you’d prefer to avoid but can’t help liking. As Melman, he was Dave’s clutch hitter, used for everything from serving as New York’s official greeter at the Port Authority to appearing in commercial parodies for Toast on a Stick.
3. DAVE’S MOM
When a man is as uncomfortable in his own skin as Letterman, few things are more squirm-inducingly funny than watching him deal with his mother. Dave’s mom Dorothy Mengering was a frequent guest, baking pies on the show every Thanksgiving and serving as a correspondent for three Olympics. Viewers lapped up her small-town charm, and she explained her appeal like this: “People enjoy seeing a mother and son together.”
4. CHRIS ELLIOTT
Late Night writer Chris Elliott was the incarnation of the show’s sense of the absurd. His characters, like the Guy Under the Seats, were often just thin disguises of his own frustrated and bitter showbiz-failure persona, made brilliant by the crumbling of Elliott’s cheery facade.
5. RUPERT JEE
Letterman smartly deputized Times Square denizens as co-stars, and Jee, owner of the Hello Deli, was up for any game or prank, including approaching strangers with a hidden earpiece and repeating whatever Letterman said.
6. RICHARD SIMMONS
Simmons was the show’s Tasmanian devil, a cheerleading dervish delivered to earth in inappropriate short shorts to make Dave cringe. Dave’s insults and Simmons’ defensive yet loving incredulity gave the pairing an opposites-attract spark.
7. MUJIBUR AND SIRAJUL
The Bangladeshi souvenir salesmen became Letterman’s roving correspondents. Stiff yet friendly in ill-fitting suits, they gave halting responses to his queries that helped serve Dave’s deconstruction of the conventional wisdom about what constitutes entertainment.
8. TONY RANDALL
One of the Late Show’s most frequent guests, with 70 appearances, Randall would stop by for a chat or surprise the audience by popping off a quick joke from the cheap seats. Randall’s acquiescent warmth created a wonderful, watchable bond with the host.
9. ALAN KALTER
A kinetic presence with psychotic tendencies, Late Show announcer Kalter became a powerful character. Kalter’s fictional (we hope) dark side kept a hostage in a metal locker and cursed Dave for ignoring him. As Letterman grew warmer and more personable, Kalter contributed a hard edge.
10. HARVEY PEKAR
Letterman and comic-book memoirist Pekar had an uneasy bond. They didn’t seem to like each other much, turning insult-filled interviews into compelling can’t-turn-away TV. Letterman once banned him from the show, but given their chemistry, it’s unsurprising that the ban didn’t last.
This appears in the May 25, 2015 issue of TIME.