Damn, that beats the Stranglers song I popped in to mention: (Get A) Grip (On Yourself).
The first song that popped into my head when I saw this thread :
**They Might Be Giants ** - “(She was a) Hotel Detective”
Not to be confused with TMBG’s “She was a Hotel Detective” which is on the Back to Skull EP and is most certainly not the same song. 
In all fairness, Elvis wasn’t responsible. Nick Lowe wrote it when he was in Brinsley Schwarz.
…and Nick loves the parentheses:
I Knew The Bride (When She Used To Rock 'N Roll)
(I Want to Build a) Jumbo Ark
12-Step Program (To Quit You Babe)
Bygones (Won’t Go)
There Will Never Be Any Peace (Until God Is Seated at the Conference Table)
Also Chris Difford and Glenn Tilbrook of Squeeze:
Hesitation (Rool Britannia)
Pulling Mussels (From the Shell)
(This Could Be) The Last Time
I’m amazed someone hasn’t gotten this yet - or maybe I am, because I certainly don’t like her, either.
Avril Lavigne - (So Much For) My Happy Ending.
I was gonna post The Offspring - (Can’t Get My) Head Around You, but someone beat me to it.
~Tasha
“I Can’t go For That (No Can Do)”–Hall & Oates
Not as superfluous as it might first appear. A “Face” was the slang term for a Mod, as referenced in numerous songs, and indeed band names, of the period: witness the Small Faces {or indeed the Faces}, or the High Number’s “I’m The Face”, which the Who included on Quadrophenia.