We show that with improved training, the standard approach for differentially private GANs -- updating the discriminator with noisy gradients -- achieves or competes with state-of-the-art results for private image synthesis. Existing instantiations of this approach neglect to consider how adding noise only to discriminator updates disrupts the careful balance between generator and discriminator necessary for successful GAN training. We show that a simple fix restores parity: taking more discriminator steps between generator steps. Finally, with the goal of restoring parity between generator and discriminator, we experiment with further modifications to improve discriminator training and see further improvements in generation quality. For MNIST at ε = 10, our private GANs improve the record FID from 48.4 to 13.0, as well as downstream classifier accuracy from 83.2% to 95.0%.