Here's a recently leaked Prince song, "Lust U Always," reportedly recorded around the same time as the 1999 album.
The music site Antiquiet says, "While the track was never used for any Prince record, His Royal Badness did end up offering it to Mr. Robert Palmer in the late 80s but the singer turned it down."
Princevault notes, "The song paraphrases some lyrics from Annie Ross's song `Twisted' (notably covered by Joni Mitchell, and later played a few times on the One Nite Alone... Tour), but thematically fits in well with much of his 1981-2 material, concerning the narrator's uncontrollable lust for a woman."
There's also a Soundcloud version that has a download link.
But as WFMU warned in a tweet today, listen quick. Prince's lawyers are likely to get this removed from Youtube pretty fast.