Avril Lavigne like her breakthrough single from 2002 is, in a word, complicated. The diminutive Canadian with the gargantuan voice has made a career sk8ing the line between pop and punk, cannily switching her target from charts to hearts and back again. For a time, it seemed the former had prevailed: 2007's The Best Damn Thing was a candy-coated collection of prefabricated, post-feminist party-starters written with proven hit-makers and halfheartedly dismissed by Avril as ''just songs'' (burn!). In contrast, Goodbye Lullaby seeks balance: The first half is loaded with glossy confections, while the second consists of quieter reflections clearly inspired by (and, bizarrely, produced by) her ex-husband, Sum 41 frontman Deryck Whibley.
Surprisingly, it's the early tunes, many concocted in the bunker of Swedish genius Max Martin, that show the most personality: The Farfisa-fueled ''What the Hell'' and the sassy ''Smile,'' with its talk of doctored drinks and blackout tattoos, restore Avril to her rightful place ahead of Katy Perry and Ke$ha in the Sisterhood of the Negligible Pants. But when left alone on gauzy ballads like ''Everybody Hurts'' (an original that somehow manages to be less deep than the R.E.M. standard) the recently divorced 26-year-old seems desperate to share an artistic inner self that's far from fully formed. ''Open up your heart...so I can show you who I am,'' she pleads on ''Stop Standing There.'' It's not us, Avril. It's you! B–