Subjective image-quality measurement plays a critical role in the development of image- processing applications. The purpose of a visual-quality metric is to approximate the results of subjective assessment. In this regard, more and more metrics are under development, but little research has considered their limitations. This paper addresses that deficiency: we show how image preprocessing before compression can artificially increase the quality scores provided by the popular metrics DISTS, LPIPS, HaarPSI, and VIF as well as how these scores are inconsistent with subjective-quality scores. We propose a series of neural-network preprocessing models that increase DISTS by up to 34.5%, LPIPS by up to 36.8%, VIF by up to 98.0%, and HaarPSI by up to 22.6% in the case of JPEG-compressed images. A subjective comparison of preprocessed images showed that for most of the metrics we examined, visual quality drops or stays unchanged, limiting the applicability of these metrics