We have measured the flux of grains from a hole in the bottom of a shaken container of grains. We find that the peak velocity of the vibration, v max, controls the flux, i.e., the flux is nearly independent of the frequency and acceleration amplitude for a given value of v max. The flux decreases with increasing peak velocity and then becomes almost constant for the largest values of v max. The data at low peak velocity can be quantitatively described by a simple model, but the crossover to nearly constant flux at larger peak velocity suggests a regime in which the granular density near the container bottom is independent of the energy input to the system.