Post-training Neural Network (NN) model compression is an attractive approach for deploying large, memory-consuming models on devices with limited memory resources. In this study, we investigate the rate-distortion tradeoff for NN model compression. First, we suggest a Rotation-Invariant Quantization (RIQ) technique that utilizes a single parameter to quantize the entire NN model, yielding a different rate at each layer, i.e., mixed-precision quantization. Then, we prove that our rotation-invariant approach is optimal in terms of compression. We rigorously evaluate RIQ and demonstrate its capabilities on various models and tasks. For example, RIQ facilitates $\times 19.4$ and $\times 52.9$ compression ratios on pre-trained VGG dense and pruned models, respectively, with $<0.4\%$ accuracy degradation. Code is available in \href{https://github.com/ehaleva/RIQ}{github.com/ehaleva/RIQ}.