Rearranging the letters of "Alanis Morissette" gives:
It's nasal, tiresome. 
Lame artist noises.
Earnest altissimo.
Ta! I'm artless noise!
SOS! I'm a senile tart! 
Mess retaliations
A real mess to sit in
Noisiest, lame star
A starlet emission
I'm a tastiness role
Am staler, noisiest
Let's! I'm a noise star
I am a tireless snot. 
Let's! Rats! I'm a noise!
I'm a reasonless tit. 
Sanest moralities. 
More Satanist lies! 
Not aimless satire.
One-mile ass artist.
Sore animal testis. 
Snot materialises
One aimless artist
A toenail mistress
Miss Sole Attaine
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Found from anagramgenius.com
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