Underwater images are often acquired in sub-optimal lighting conditions, in particular at profound depths where the absence of natural light demands the use of artificial lighting. Low-lighting images impose a challenge for both manual and automated analysis, since regions of interest can have low visibility. A new framework capable of significantly enhancing these images is proposed in this article. The framework is based on a novel dehazing mechanism that considers local contrast information in the input images, and offers a solution to three common disadvantages of current single image dehazing methods: oversaturation of radiance, lack of scale-invariance and creation of halos. A novel low-lighting underwater image dataset, OceanDark, is introduced to assist in the development and evaluation of the proposed framework. Experimental results and a comparison with other underwater-specific image enhancement methods show that the proposed framework can be used for significantly improving the visibility in low-lighting underwater images of different scales, without creating undesired dehazing artifacts.