There is a song by an Australian band called The Hoodoo Gurus called "Bittersweet," but the song itself isn't bittersweet -- it rocks. It's one of my all time favorite rock and roll songs with three chords, a good beat, and a lot of energy and exhuberance.

"Keeping Awake" by the Innocence Mission is sort of bittersweet. Another Beatles number that's bittersweet is "In My life." So is Stan Getz "Corcovado (Quiet Nights of Quiet Stars)", almost. [see the thread on beauty in all its forms].

I like "Corcovado" because it illustrates how a person in love changes from a pessimist (if they were one to begin with) to an optimist:

I who was lost and lonely, believing life was only
a bitter, tragic joke have found with you
the meaning of existence, oh my love..."

At the end of the second line, when the word "you" is sung, it's the most beautiful note in the whole song. Such an amazing composition -- and to think the lyrics in English are just the translation from the original Portuguese!