Recent Earth observation satellite projects, in particular the Pleiades project (to be launched in 2010) contemplate the acquisition of quasi-simultaneous stereo pairs. This paper evaluates the impact of the (necessary) compression of the stereo pairs. It compares two compression strategies. The first compression strategy uses classic JPEG 1992 or JPEG 2000, which retain the best perceptual performance. The second compression strategy maintains a shift invariance by simply sub-sampling both views after applying an anti-aliasing Gaussian filter. The quantitative comparison of these two basic strategies shows that JPEG algorithms must compress twice less than sub-sampling to reach the same disparity precision. This dramatic result is explained by the lack of translation invariance of classic compression algorithms. Nonetheless, the sweeping conclusion is that shift invariant algorithms are better compression tools for future stereo Earth observation satellites.