A method of operating a gaming system, said gaming system including a controller in communication with a plurality of gaming machines wherein each gaming machine includes a primary game operable upon a wager placed by a player, said method comprising:
- (a) causing the controller to maintain a plurality of progressive awards;
- (b) after an occurrence of a random triggering event in association with at least one of the gaming machines, regardless of any amounts of the wagers placed by the players on plays of the primary game, enabling one of the players to directly select any one of the maintained progressive awards as a first progressive award during a play of a secondary game;
- (c) enabling said player to play for the selected first progressive award at a first time during the play of the secondary game;
- (d) determining whether to provide the selected first progressive award to said player;
- (e) regardless of if said player is provided the selected first progressive award, enabling said player to play for a second progressive award at a second, different time during the same play of the secondary game;
- and
- (f) determining whether to provide the second progressive award to said player.