A gaming system is primarily dedicated to playing a regulated casino wagering game providing eligibility to a plurality of progressive jackpots. The gaming system comprises a secure gaming cabinet, an electronic display device, an electronic input device, a random element generator, and game-logic circuitry. The game-logic circuitry is configured to allocate a portion of the wager to at least one of a first group of progressive jackpots, direct the electronic display device to increment the value of the first group of progressive jackpots, and direct the electronic display device to increment the values of a second group progressive jackpots based on the values of the first group of progressive jackpots. And, in response to a progressive-triggering outcome, the game-logic circuitry directs the electronic display device to display a reset value for the awarded progressive jackpot and an altered reduced value for another one of the progressive jackpots.