What Tango said! I don't know how you came to the conclusion that it's only running 1/2 compression, can you elaborate on that one please? If you run it with a dead battery then there's a good chance that you're not getting enough of a spark which will lead to rough running so let us know what happens once you bung the new one on. It does sound electrical or maybe the valves but without doing some diagnostics on it, it's really difficult to find out anything further - if you have a voltmeter handy then there are a few tests you can do to check the electrical system. The fact that you rode it home fine on day one makes me think it's just a dud battery so it's worth checking the charging system once you've got the new one on. Also, I wouldn't worry about the state of your plugs just yet, it takes a good few miles to get any colour on them unless you're running outrageously rich! On that note, have you checked the fuel filter? It could be that it's bunged up with crud but that wouldn't explain the backfiring... Finally, where are you? Cheers, Fro