Depp, star of "Edward Scissorhands" and the "Pirates of the Caribbean" movies, portrays a murderous barber in the macabre new movie musical, while Rickman plays the man who ruined his life.
"Well, having worked with sharp objects before, everything was fine until I had to shave someone," Depp told reporters in London recently.
Director Tim Burton said his long-time friend didn't have any trouble handling the razors.
"He was freaked out by the shaving cream. Am I right?" Burton challenged Depp. "Was that the hardest thing you had to do? Lather up Alan Rickman?"
Depp admitted it was, saying, "That was one of the most uncomfortable moments of my life."
Burton then recalled how Depp approached him and told him: "I can't do it. I can't. I can't."
"Poor Alan," Depp said. "(Alan) really didn't enjoy it. ... So, in that sense, I'm sure he didn't enjoy working with me."
Celebrity Families of 2014 [PHOTOS]