A gaming device having an improved award-providing bonus scheme wherein the player may improve their award during different rounds of the bonus scheme. The gaming device enables the player to select an award from a plurality of awards. The gaming device enables the player to modify the selected award, creating a subsequent or modified award, and carry over residual award improvements from one round to a different round of the bonus game, with the idea of increasing the award to receive a greater or higher award during the bonus game.