Yes Sir and his mother, Mae , co-wrote "Heartbreak Hotel" with Tommy Durden.
I was about to add my two cents (or less) worth a week ago when my computer's hard drive threw up. Just got it back today, so better late than never I guess.
As long as we are/were talking about who wrote what for Elvis, we must not forget Dolores Fuller, who wrote or co-wrote a dozen or so songs for the King. Some of the titles were "Rock-A-Hula Baby," "I Got Lucky", "Spinout" and "Do The Clam." She also wrote a couple numbers recorded by Nat King Cole and Peggy Lee.
Ms. Fuller probably was most famous, at least in later years, for her appearances in three films written and directed by her then boyfriend, Edward D. Wood Jr. The films -- "Glen or Glenda" (where, in real life, she discovered Wood was a cross-dresser), "Jail Bait" and "Bride of the Monster."
Supposedly, Wood wanted to marry Dolores but she couldn't deal with his angora fetish, so she wound up a songwriter.
If all goes well, here is a still of Dolores and Ed from "Glen or Glenda."