Image compression systems that exploit the properties of the Human Visual System (HVS) have been studied extensively over the few decades. For the JPEG2000 image compressionstandard, several methods to optimize perceptual quality have been proposed. In 2013, Han et al. proposed a visually lossless compression approach based on the irreversible pipeline defined in the JPEG2000 standard. In this approach, visibility thresholds were measured using psychovisual experiments. These thresholds were then incorporated in a JPEG2000 encoder to ensure that quantization distortions remain below visible levels in the compressed codestreams. In this work, we investigate the use of a similar approach for the reversible pipeline of the JPEG2000 standard. Our motivation is to allow the creation of a scalable codestream that can provide both visually lossless and numerically lossless representations from a single codestream. By comparing the difference in compression performance between the reversible and irreversible pipelines, we also quantify the overhead associated with the reversible pipeline for visually lossless compression.