Visually lossless coding is a method through which an image is coded with numerical losses that are not noticeable by visual inspection. Contrary to numerically lossless coding, visually lossless coding can achieve high compression ratios. In general, visually lossless coding is approached from the point of view of the encoder, i.e., as a procedure devised to generate a compressed code stream from an original image. If an image has already been encoded to a very high fidelity (higher than visually lossless - perhaps even numerically lossless), it is not straightforward to create a just visually lossless version without fully re-encoding the image. However, for large repositories, re-encoding may not be a suitable option. A visually lossless decoder might be useful to decode, or to parse and transmit, only the data needed for visually lossless reconstruction. This work introduces a decoder for JPEG 2000 code streams that identifies and decodes the minimum amount of information needed to produce a visually lossless image. The main insights behind the proposed method are to estimate the variance of the code blocks before the decoding procedure, and to determine the visibility thresholds employing a well-known model from the literature. The main advantages are faster decoding and the possibility to transmit visually lossless images employing minimal bit rates.