A gaming system including a central server linked to a plurality of gaming machines is provided. The gaming system includes a plurality of progressive awards arranged in a hierarchy. Upon the occurrence of a triggering event or qualifying condition, a bonus game is started. A player can win a next higher progressive award by accumulating award values. If the player's total award value is greater than or equal to a trigger value for a progressive award, the player wins the progressive award. Unless a termination condition occurs, the bonus game continues. The total award value is set to the progressive award value. Alternatively, the progressive award value is added to the player's total award value. The trigger value for a progressive award can be the startup value for that progressive award.