Rich was notoriously short-tempered. Singer Dusty Springfield slapped him after several days of "putting up with Rich's insults and show-biz sabotage". He held a rivalry with Frank Sinatra which sometimes ended in brawls when both were members of Tommy Dorsey's band. Nevertheless, they remained lifelong friends, and Sinatra delivered a eulogy at Rich's funeral in 1987. In 1983, Rich underwent quadruple bypass surgery, and was often visited by Sinatra in hospital. Billy Cobham said that he met Rich in a club and asked him to sign his snare drum, but Rich "dropped it down the stairs".