Helium-shell flashes have been studied in stars with a total mass Msun of 0.8, 1.0,2.0, and 3.0 Msun and hydrogen-depleted core masses Mc in the range 0.53-0.9 Msun. Particular attention was focused on the variation in surface luminosity resulting from the flash, since the peak surface luminosity during the flash cycle plays an important role in determining the termination point of asymptotic giant branch evolution. It was found that both the peak in surface luminosity at the flash (LP) and the quiescent luminosity maximum (LQ) occurring between each shell flash increase linearly with core mass. However, LP and LQ are shown to be independent of total stellar mass in the range of masses studied because envelope convection does not penetrate far enough into the star. Formulae are given for the dependence on MC of LP, LQ, the interpulse period, and the length of the interval during which the surface luminosity at the flash exceeds the quiescent maximum. Approximate formulae for the time dependence of the surface luminosity are also given. Rates of period change in the Mira variables R Hya, R Aql, and W Dra are compared with rates of change predicted by theoretical flash calculations and, as a result, constraints on the luminosity of these stars are derived via the theoretical relation between luminosity and rate of change of luminosity. The luminosities thus derived for R Hya and R Aql are compared with luminosities derived from pulsation theory.