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Alot of their songs are covers.
Imagine my surprise when I heard the original "Shoehorn with Teeth" (from TMBG's Lincoln album.)
I was a bit let down that they hadn't written it (this was years ago).
Didn't realize that Istanbul not Constatinople wasn't written by them though. >>
Umm.. No. "The Guitar" was not a cover, but they did borrow enough of "Lion Sleeps Tonight" to have to credit the authors of that song. It's like when The Verve looped the riff of a Rolling Stones song (I forget the song) on "Bitter Sweet Symphony". Jagger and Richards sued The Verve Pipe to get credit for the riff.
First album: All songs by TMBG (C)1987
Lincoln: All songs by TMBG (C) 1988 INCLUDING "Shoehorn with Teeth". Whoever told you it wasn't their song was LYING! Would someone other than TMBG write a song with a lyric that says "people should get beat up for stating their beliefs?"
Flood: All songs by TMBG (C) 1990 except "Istanbul" (C) 1953 J. Kennedy N. Simon
Apollo 18: All songs by TMBG (C) 1992 "The Guitar" portions of "Lion Sleeps Tonight" (Hardly a cover. No writing credit or copyright credit given either) used by permission
John Henry: All songs by TMBG (C) 1994 TMBG II Should Be Allowed To Think" contains first line of "Howl: Part One" by Allen Ginsberg (C) 1956
Here's where I was wrong about my statement that they only had one cover on a full album:
Factory Showroom: All songs by TMBG (C)1996 except "New York City" (C) (no date or original artist given/found) Paw-Paw Publishing :Q
NOOOOOOOOOOOO! I WAS WRONG ABOUT SOMETHING!:Q First time ever!!! Ok... Second time this week.
Mink Car: All songs by TMBG (C) 2001 except "Yeh Yeh" (C) 1964 apparently was a Georgie Fame song. Go figure. Didn't know about that one!
Of course, singles, live albums and EPs don't count, because if they did you'd have The Joker, Why Does The Sunshine, Frankenstein.......
So there you go. Seven albums and only THREE cover songs.

Two songs with enough samples to credit the original.
Anyone else up for more TMBG trivia?