Hyperspectral image (HSI) denoising has achieved promising results with the development of deep learning. A mainstream class of methods exploits the spatial-spectral correlations and recovers each band with the aids of neighboring bands, collectively referred to as spectral auxiliary networks. However, these methods treat entire adjacent spectral bands equally. In theory, clearer and nearer bands tend to contain more reliable spectral information than noisier and farther ones with higher uncertainties. How to achieve spectral enhancement and adaptation of each adjacent band has become an urgent problem in HSI denoising. This work presents the UA-Adjustor, a comprehensive adjustor that enhances denoising performance by considering both the band-to-pixel and enhancement-to-adjustment aspects. Specifically, UA-Adjustor consists of three stages that evaluate the importance of neighboring bands, enhance neighboring bands based on uncertainty perception, and adjust the weight of spatial pixels in adjacent bands through estimated uncertainty. For its simplicity, UA-Adjustor can be flexibly plugged into existing spectral auxiliary networks to improve denoising behavior at low cost. Extensive experimental results validate that the proposed solution can improve over recent state-of-the-art (SOTA) methods on both simulated and real-world benchmarks by a large margin.