Are end-to-end text-to-speech (TTS) models over-parametrized? To what extent can these models be pruned, and what happens to their synthesis capabilities? This work serves as a starting point to explore pruning both spectrogram prediction networks and vocoders. We thoroughly investigate the tradeoffs between sparsity and its subsequent effects on synthetic speech. Additionally, we explored several aspects of TTS pruning: amount of finetuning data versus sparsity, TTS-Augmentation to utilize unspoken text, and combining knowledge distillation and pruning. Our findings suggest that not only are end-to-end TTS models highly prunable, but also, perhaps surprisingly, pruned TTS models can produce synthetic speech with equal or higher naturalness and intelligibility, with similar prosody. All of our experiments are conducted on publicly available models, and findings in this work are backed by large-scale subjective tests and objective measures. Code and 200 pruned models are made available to facilitate future research on efficiency in TTS.