Today's generative neural networks allow the creation of high-quality synthetic speech at scale. While we welcome the creative use of this new technology, we must also recognize the risks. As synthetic speech is abused for both monetary and identity theft, we require a broad set of deep fake identification tools. Furthermore, previous work reported a limited ability of deep classifiers to generalize to unseen audio generators. By leveraging the wavelet-packet and short-time Fourier transform, we train excellent lightweight detectors that generalize. We report improved results on an extension of the WaveFake dataset. To account for the rapid progress in the field, we additionally consider samples drawn from the novel Avocodo and BigVGAN networks.