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This paper presents an approach for providing the desired visually lossless quality of Joint Photographic Experts Group (JPEG) and Versatile Video Coding (VVC) compressed images. The desired quality is defined as the peak signal-to-noise ratio (PSNR) of the first just noticeable difference (JND) point, which represents the boundary between visually lossless and visually lossy image compression. The proposed approach is based on a piecewise linear interpolation of the PSNR as a function of the parameter that controls the degree of compression—the quality factor (QF) or the quantization parameter (QP). The desired quality is obtained by determining the PSNR value for only two or three values of the QF or QP. The accuracy of the proposed approach was investigated on three publicly available image databases with available results of subjective JND tests on nearly 300 high-resolution images. It has been shown that the maximum difference between the desired and provided quality of JPEG compressed images is 0.3 dB, while the maximum difference in images with VVC compression is slightly larger and is approximately 0.5 dB. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.