I really like Twilight Imperium (3rd edition), but I haven't really enjoyed my time playing it due to the long playtimes. I've played one 4-player game, two 6-player, and one 8-player game. The shortest game was the 4p - it clocked in at 6.5 hours. And that was with experienced players. I don't feel like anyone had serious Analysis Paralysis during the game but approximately one hour per full game round is just ridiculous.
One option is to play the variant where everyone starts with several systems (neighbor systems are just given to you for free). I do enjoy the early expansion part of the game, so I'm leery about trying that. Are there any other suggestions for speeding up play?