In imaging systems, following acquisition, an image/ video is transmitted or stored and eventually presented to human observers using different and often imperfect display devices. While the resulting quality of the output image may severely be affected by the display, this degradation is usually ignored in the preceding compression. In this paper we model the sub-optimality of the display device as a known degradation operator applied on the decompressed image/video. We assume the use of a standard compression path, and augment it with a suitable pre-processing procedure, providing a compressed signal intended to compensate the degradation without any post-filtering. Our approach originates from an intricate rate-distortion problem, optimizing the modifications to the input image/video for reaching best end-to-end performance. We address this seemingly computationally intractable problem using the alternating direction method of multipliers (ADMM) approach, leading to a procedure in which a standard compression technique is iteratively applied. We demonstrate the proposed method for adjusting HEVC image/video compression to compensate post-decompression visual effects due to a common type of displays. Particularly, we use our method to reduce motion-blur perceived while viewing video on LCD devices. The experiments establish our method as a leading approach for preprocessing high bit-rate compression to counterbalance a postdecompression degradation.