Local backlight dimming (LBD) is a promising technique for improving the contrast ratio and saving power consumption for liquid crystal displays. LBD consists of two crucial parts, i.e., backlight luminance determination, which locally controls the luminance of each sub-block of the backlight unit (BLU), and pixel compensation, which compensates for the reduction of pixel intensity, to achieve pleasing visual quality. However, the limitations of the current deep learning–based pixel compensation methods come from two aspects. First, it is difficult for a vanilla image-to-image translation strategy to learn the mapping relations between the input image and the compensated image, especially without considering the dimming levels. Second, the extensive model parameters make these methods hard to be deployed in industrial applications. To address these issues, we reformulate pixel compensation as an input-specific curve estimation task. Specifically, a deep lightweight network, namely, the curve estimation network (CENet), takes both the original input image and the dimmed BLUs as input, to estimate a set of high-order curves. Then, these curves are applied iteratively to adjust the intensity of each pixel to obtain a compensated image. Given the determined BLUs, the proposed CENet can be trained in an end-to-end manner. This implies that our proposed method is compatible with any backlight dimming strategies. Extensive evaluation results on the DIVerse 2K (DIV2K) dataset highlight the superiority of the proposed CENet-integrated local dimming framework, in terms of model size and visual quality of displayed content.