Large language models (LLMs) possess incredible potential, but fine-tuning them for specific tasks remains computationally expensive. Imagine training a model with billions of parameters—it's a resource-intensive process that requires powerful hardware. However, a new wave of efficient fine-tuning techniques is changing this landscape. One such approach, Sparse Parameter-Efficient Fine-Tuning (SPEFT), strategically updates only a small fraction of the model's most important parameters. This research dives into refining SPEFT by exploring which parameters matter most and how to identify them efficiently. The study systematically evaluates various methods for selecting these key parameters, drawing inspiration from network architecture search techniques. Surprisingly, simple gradient-based metrics prove highly effective at pinpointing the most impactful weights, even outperforming more complex, computationally expensive methods. The research also challenges the assumption that constantly updating the selection of these parameters is necessary. Results reveal that a static selection, chosen before training even begins, can achieve similar or even better performance, significantly boosting efficiency. This streamlined approach simplifies the fine-tuning process, making it more accessible and efficient. As specialized hardware for sparse computations becomes increasingly common, SPEFT is poised to become even more powerful, allowing us to unlock the full potential of LLMs in diverse real-world applications.