Abstract-This letter proposes a method for lossless coding the left disparity image, L, from a stereo disparity image pair (L,R), conditional on the right disparity image, R, by keeping track of the transformation of the constant patches from R to L. The disparities in R are used for predicting the disparities in L, and the locations of the pixels where the prediction is erroneous are encoded in a first stage, conditional on the patch-labels of R image, allowing the decoder to already reconstruct with certainty some elements of the L image, e.g., the disparity values at certain pixels and parts of the contours of left image patches. Second, the contours of the patches in L image that are still unknown after first stage are conditionally encoded using a mixed conditioning context: the usual causal current context from the contours of L and a noncausal context extracted from the contours in the correctly estimated part of L obtained in the first stage. The depth values in the patches of L image are finally encoded, if they are not already known from the prediction stage. The new algorithm, dubbed conditional crack-edge region value (C-CERV), is shown to perform significantly better than the non-conditional coding method CERV and than another existing conditional coding method, over the Middlebury corpus. C-CERV is shown to reach lossless compression ratios of 100-250 times for those images that have a high precision of the disparity map.