An inflatable sport ball, such as a basketball, a football, a soccer ball, a volleyball or a playground ball, is provided with a self-contained inflation mechanism, or multiple self-contained inflation mechanisms, for inflating or more likely adding pressure to the ball. The pump additionally contains an integral pressure relief device to release air and relieve the pressure of the ball and/or a pressure-indicating device to determine the relative pressure of the ball. The mechanism is a pump which is inside of the ball and which is operable from outside of the ball to pump ambient air into the ball.