We investigate data compression schemes for proposed all-sky diffraction-limited visible/NIR sky surveys aimed at the dark-energy problem. We show that lossy square-root compression to 1 bit pixel-1 of noise, followed by standard lossless compression algorithms, reduces the images to 2.5–4 bits pixel-1, depending primarily upon the level of cosmic-ray contamination of the images. Compression to this level adds noise equivalent to ≤ 10% penalty in observing time. We derive an analytic correction to flux biases inherent to the square-root compression scheme. Numerical tests on simple galaxy models confirm that galaxy fluxes and shapes are measured with systematic biases ≲10-4 induced by the compression scheme, well below the requirements of supernova and weak gravitational lensing dark-energy experiments. In a related investigation, Vanderveld and coworkers bound the shape biases using realistic simulated images of the high-Galactic–latitude sky. The square-root preprocessing step has advantages over simple (linear) decimation when there are many bright objects or cosmic rays in the field, or when the background level will vary.