We simulate the collapse of isolated dwarf galaxies using SPH + N-Body simulations including a physically motivated description of the effects of supernova feedback. As the gas collapses and stars form, the supernova feedback disrupts enough gas to temporarily quench star formation. The gas flows outward into a hot halo, where it cools until star formation can continue once more and the cycle repeats. The star formation histories of isolated Local Group dwarf galaxies exhibit similar episodic bursts of star formation. We examine the mass dependence of the stellar velocity dispersions and find that they are no less than half the velocity of the halos measured at the virial radius.