Neil Hannon, of the Divine Comedy, is a songwriter I admire greatly. I know this because I listen to his music and enjoy it, and because I forgive him for some transgressions against pure rhyme that, in lesser songwriters, I'd probably make a massive stand against. The thing he does, and it's quite common, is rhyme on the long vowel and the combination of letters on the end of the word, but not necessarily keep the integrity of the sound after the vowel. The classic example of this is in the song "Songs of Love":

"Pale, pubescent beasts,
roam through the streets"

So, there's the "eeee" sound and the "sts", but the word "streets" has a sort of sibilant ending, but it's different. The pure rhyme for "beasts" might be "yeasts" or "feasts". Yet, I don't seem to mind. In the song "Come Home Billy Bird", there's a load of these misformed rhymes, until the very denouement of the song, where the rhymes go pure. I don't know if Mr Hannon intentionally sets his lyrics against the grain of the perfect rhyme in some places, maybe in "Come Home..." he's doing it to represent the stress of the "international business traveller". Maybe not.

Anyway, I like The Divine Comedy, and anyone who doesn't is wrong.