Compressive adaptation approaches, such as QLoRA, are widely popular alternatives for reducing memory requirements during fine-tuning of large language models (LLMs) while producing models capable of handling various downstream tasks. The key idea is to employ a "two-tower" architecture: compressing pre-trained LLM parameters into compact representations and fine-tuning the additive full-precision adapter, which typically has few tunable parameters in low-rank format. However, the strict algebraic assumptions, such as low-rank assumption, and the complexity of composing two-tower architectures are some of the known shortcomings, resulting in a poor accuracy-efficiency trade-off. In response to these known limitations, we propose SpaLLM (Sketched Parameter Adaptation of LLMs), a novel compressive adaptation approach for LLMs. This method is also the first to illustrate parameter-sharing compression methods for LLM fine-tuning, which, unlike QLoRA, are free from strict low-rank algebraic assumptions on adapters. Furthermore, our proposal unifies model compression and adaptation into a single, streamlined process, eliminating the need for two-tower architectures. SpaLLM sketches pre-trained LLM weights into lookup tables and directly fine-tunes the values in these tables. This approach simplifies LLMs' compressive adaptation workflow, potentially improves multi-user serving efficiency, and delivers significantly better accuracy for both natural language understanding and generation tasks. Moreover, by avoiding the "two-tower" architecture, our framework only requires one compressed matrix multiplication per layer during inference, demonstrating superior inference efficiency compared to previous methods.