Also, the jump height will never be exactly the same from one jump to another. This was a big issue in a game I made where a 10 pixels variation was too much. The solution I came up with was to have an invisible solid object always located at a certain height over the character to stop it from jumping higher.
Of course, when FPS gets really low, anything's still possible... (as my tester found out when trying my game on an old computer at about 10 or 15 FPS, which resulted in very funny glitches, such as the character flying around the place)