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We studied the performance of linear scatter correction methods for single-photon imaging with Tc-99m and Tl-201, using a numerical model of the Rollo phantom and measurements with a gamma camera modified to record position and energy information in list mode form. We compared the performance of these methods to per-image optimized linear methods and to locally adaptive linear methods, and developed estimates of the limits on accuracy of scatter correction imposed by the presence of Poisson noise. For both Tc-99m and Tl-201 imaging at a fixed depth, particularly at low count rates, the performance of dual-window methods, or of adaptive methods, is near the best possible for linear methods. Smoothing of the scatter estimate results in minor improvement for Tl-201. Substantial gaps between the performance of any of these linear methods and the limits imposed by Poisson noise remain and are due primarily to bias, with the gap for Tl-201 being larger than that for Tc-99m.