In this paper, a novel method is presented for producing energy-efficient images, i.e., images that consume less electrical energy on energy-adaptive displays, yet have the same or very similar perceptual quality to their original images. The proposed method relies on the fact that the energy consumption of pixels in modern energy-adaptive displays like OLED displays is directly proportional to the luminance of the pixels. Hence, in this paper, to reduce the energy consumption of an image, while at the same time preserving its perceptual quality, it is proposed to reduce the luminance of the pixels in the image by one just-noticeable-difference (JND) threshold. To determine the JND thresholds, an adaptive saliency-modulated JND (SJND) model is developed. In the proposed model, the JND thresholds of each block in the given image are elevated by two non-linear saliency modulation functions using the visual saliency of the block. The parameters of the saliency modulation functions are estimated through an adaptive optimization framework, which utilizes a state-of-the-art saliency-based objective image quality assessment method. To evaluate the proposed methods, a set of subjective experiments were conducted, and the real energy consumption of the produced energy-efficient images were measured by an accurate power monitor equipment on an OLED display. The obtained experimental results demonstrated that, on average, the proposed method is able to reduce the energy consumption by about 14.1% while preserving the perceptual quality of the displayed images.