I hate Tournament so much it would be a crime to mention any other card in the same breath. It... is... so... random.
The concept behind Tournament is great, but many feel its execution is awful. A non-attack card that interacts with other players is a rarity in Dominion; the variety and accomplishment of winning prizes is clever.
Tournament should create a side game, like gambling in the game Red Dragon Inn.
Here's an idea I had for it:
Whenever Tournament is in the supply, all players start with one card in their starter deck as well (replacing a copper). When someone wants to start a Tournament, he plays it and anyone else with a Tournament in his hand may then play it as well, joining the match. Then every player takes one remaining card from his hand and secretly "bids" -- the person who bid the highest card wins.
(In the case of a tie, do a rock-paper-scissors thing, with green cards beat actions, actions beat treasures, treasures beat green cards -- this would require a rule to deal with dual-type cards.) Then after the tournament, everyone draws a card to replace the one they bid with.
Whoever wins gets a prize which he draws RANDOMLY (reducing the time it takes to decide which to pick), places on the top of his deck, and returns to the prize pile during clean-up.
This design may not work, so I thought y'all could help me refine it.