This started off as a comment to kjorteo, but I got so caught up in it that I made a post out of it (and it means there's something other than pigeon-related material on my journal, a rare occasion so far this year). Heavenly have been one of my favourite bands for a while, but it took three albums for me to really notice them after I first found their MP3s on Noise Records. They've never quite been... straightforward, but on listening to their early albums again I'm increasingly convinced that Ben Sotto just had no idea how to write music at this stage - and as a result, being uninfluenced by traditions, his songs stand out as being among the most unique in terms of song structure that I've heard (quite apart from having the only band I know to be named as an adjective).
Still Believe, for example, is a complete mess. Most four or five-minute rock songs can loosely be said to fit into an ABABCB pattern, a rotation of verses and chorus with a different C-section in the middle, but this one... notably doesn't. This is my dissection:
It starts off with a fanfare-like section that slides into a 6/8-time introduction before abandoning that and changing time again when the vocals start, in a pair of two lines that alternate between fast and slow drum patterns twice in their short duration. There's something slightly odd about the melody of these lines when taken in isolation, for a reason that will become clear later - for now, another switch is performed into something that would probably be called a verse if this section appeared more than once. After playing that in two different keys, the melody from the pre-verse reappears again, but it starts on the second line, then goes into a different section instead and becomes a pre-chorus.
From the chorus, things calm down a little (time changes during the chorus notwithstanding), and a post-chorus choir/solo section leads to the C-section (where I would be convinced there was a female vocalist if this were anybody else). The C-section is repeated with a sort of... flourish/chorus-like bit in between, after which the song goes back to its start and finally the pre-chorus gets to play in its entirety - the two lines from the beginning of the song leading into the section in the middle. After that, the first chorus reappears, and the post-chorus is replayed to form the ending.
A - Intro 1