A major issue in telepathology is the extremely large and growing size of digitized "virtual" slides, which can require several gigabytes of storage and cause significant delays in data transmission for remote image interpretation and interactive visualization by pathologists. Compression can reduce this massive amount of virtual slide data, but reversible (lossless) methods limit data reduction to less than 50%, while lossy compression can degrade image quality and diagnostic accuracy. "Visually lossless" compression offers the potential for using higher compression levels without noticeable artifacts, but requires a rate-control strategy that adapts to image content and loss visibility. We investigated the utility of a visual discrimination model (VDM) and other distortion metrics for predicting JPEG 2000 bit rates corresponding to visually lossless compression of virtual slides for breast biopsy specimens. Threshold bit rates were determined experimentally with human observers for a variety of tissue regions cropped from virtual slides. For test images compressed to their visually lossless thresholds, just-noticeable difference (JND) metrics computed by the VDM were nearly constant at the 95th percentile level or higher, and were significantly less variable than peak signal-to-noise ratio (PSNR) and Structural Similarity (SSIM) metrics. Our results suggest that VDM metrics could be used to guide the compression of virtual slides to achieve visually lossless compression while providing 5 to 12 times the data reduction of reversible methods.