Tony Randall had many great supporting roles

To recent generations, he was known for the persnickety fussbudget he played on TV’s “Odd Couple.” But Tony Randall, who died last week, was one of the all-time great supporting actors on the American screen.

Here’s a trio of Randall pictures worth renting:

• “Will Success Spoil Rock Hunter?” (1957, 93 minutes): Randall stars as a put-upon advertising executive who persuades a starlet (Jayne Mansfield) to endorse one of his products in exchange for his pretending to be her lover. This surprisingly still-funny satire proved that as gracefully as Randall supported bigger stars, he was capable of carrying a movie on his own.

• “Pillow Talk” (1959, 103 minutes): This Rock Hudson-Doris Day vehicle featured Randall in a career-defining performance as the sardonically funny sidekick. Day plays an interior decorator engaged to Randall’s millionaire theater producer; Hudson portrays a songwriter who shares a party line with Day’s character and is being backed by Randall. It defines 1950s romantic comedy, thanks in large part to Randall’s impeccable timing and portrait of sad-eyed resignation.

• “Down With Love” (2003, 101 minutes): It received middling reviews, but this contemporary parody of Day-Hudson comedies features Randall in his last movie role. Renee Zellweger and Ewan McGregor star as the sparring couple, while David Hyde Pierce assumes Randall’s mantle as the fussy best friend. (Rated PG-13 for sexual humor and dialogue.)