To address the challenges of deploying large-scale language models (LLMs) in resource-constrained environments, this paper proposes NoWag (Normalized Weight and Activation Guided Compression), a unified framework for zero-shot shape-preserving compression algorithms. NoWag compresses Llama-2 7B/13B/70B and Llama-3 8B/70B models using two forms of shape-preserving compression: vector quantization (NoWag-VQ) and unstructured/semi-structured pruning (NoWag-P). Experimental results show that NoWag-VQ significantly outperforms state-of-the-art zero-shot vector quantization methods, and NoWag-P is competitive with them. These results suggest commonalities between the two compression paradigms for future research. The source code is available on GitHub.