BillG wrote: 
Well researched. Alanis owes me $5.00 for my glowing (but misinformed) critique of a great song.
Apologies to Gomez. You get 15% royalties...

 BKEvans wrote: 
"Uninvited" was released in 1997.
"How We Operate" was released in 2007.

2 different melodies, too — to my ear, anyway. 

About being Uninvited

I find Alanis Morissette's early work to be affected. However, she has improved, having shed herself of that signature up-glide at the end of every phrase. I respect her talent. And then I hear "Uninvited".
    I am transfixed. The crescendo untying a perfect, simple melody. This is genius. What has she been doing in the cocoon of pretentious alternative rock. I get the link and listen again and again.
     This is a burning bush of affirmation. But it just isn't Alanis Morissette's style. It is a Picasso done by Norman Rockwell. Sometimes it just doesn't make sense.
      Then I am listening to my favorite streaming radio station, Radio Paradise. On comes a single banjo. He is plucking out single notes. An electronic version of the tune sets a pulse. A guy with a sort of raspy nasal voice starts singing. It builds simply but perfectly. It is a song by "Gomez" called "How to Operate". I am listening to Alanis Morissette's song lyrics changed but the melody and phrasing is identical.
       Alanis Morissette didn't write "Uninvited". She orchestrated Gomez's "How to Operate", put a very pretty girl into a Queens gown and sold it as her own. Gomez gets nothing. I have researched it and Alanis has cooped the same song. I love these mysteries. Gomez and the DJ's at Radio Paradise know the truth. Alanis knows how to hide it.
     Tough thing when art becomes artifice. Hope you get a chance to hear them both.