Visual data play a crucial role in modern society, and the rate at which images and videos are acquired, stored, and exchanged every day is rapidly increasing. Image compression is the key technology that enables storing and sharing of visual content in an efficient and cost-effective manner, by removing redundant and irrelevant information. On the other hand, image compression often introduces undesirable artifacts that reduce the perceived quality of the media. Subjective image quality assessment experiments allow for the collection of information on the visual quality of the media as perceived by human observers, and therefore quantifying the impact of such distortions. Nevertheless, the most commonly used subjective image quality assessment methodologies were designed to evaluate compressed images with visible distortions, and therefore are not accurate and reliable when evaluating images having higher visual qualities. In this paper, we present a dataset of compressed images with quality levels that range from high to nearly visually lossless, with associated quality scores in JND units. The images were subjectively evaluated by expert human observers, and the results were used to define the range from high to nearly visually lossless quality. The dataset is made publicly available to researchers, providing a valuable resource for the development of novel subjective quality assessment methodologies or compression methods that are more effective in this quality range.