With the increasing exploration and exploitation of the underwater world, underwater images have become a critical medium for human interaction with marine environments, driving extensive research into their efficient transmission and storage. However, contemporary underwater image compression algorithms fail to adequately address the impact of water refraction and scattering on light waves, which not only elevate training complexity but also result in suboptimal compression performance. To tackle this limitation, we propose High Quality Underwater Image Compression (HQUIC), a novel framework designed to handle the unique illumination conditions and color shifts inherent in underwater images, thereby achieving superior compression performance. HQUIC first incorporates an Adaptive Lighting and Tone Correction (ALTC) module to adaptively predict the attenuation coefficients and global light information of images, effectively alleviating issues stemming from variations in illumination and tone across underwater images. Secondly, it dynamically weights multi-scale frequency components, prioritizing information critical to distortion quality while discarding redundant details. Furthermore, we introduce a tone adjustment loss to enable the model to better balance discrepancies among different color channels. Comprehensive evaluations on diverse underwater datasets validate that HQUIC outperforms state-of-the-art compression methods, demonstrating its effectiveness.