We present an algorithm to reduce per-pixel search ranges for Markov Random Fields-based stereo algorithms. Our algorithm is based on the intuitions that reliably matched pixels need less regularization in the energy minimization and neighboring pixels should have similar disparity search ranges if their pixel values are similar. We propose a novel bi-labeling process to classify reliable and unreliable pixels that incorporate left-right consistency checks. We then propagate the reliable disparities into unreliable regions to form a complete disparity map and construct per-pixel search ranges based on the difference between the disparity map after propagation and the one computed from a winner-take-all method. Experimental results evaluated on the Middlebury stereo benchmark show our proposed algorithm is able to achieve 77% average reduction rate while preserving satisfactory accuracy.