Distortions of the root3 x root3- Sn/Ge(111) and Sn/Si(111) surfaces are shown to reflect a disproportionation of an integer pseudocharge, Q, related to the surface band occupancy. A novel understanding of the (3 x 3)-1U ("1 up, 2 down") and 2U ("2 up, 1 down") distortions of Sn/Ge(111) is obtained by a theoretical study of the phase diagram under strain. Positive strain keeps the unstrained value Q = 3 but removes distortions. Negative strain attracts pseudocharge from the valence band causing first a (3 X 3)-2U distortion (Q = 4) on both Sn/Ge and Sn/Si, and eventually a (root3 x root3)-3U ("all up") state with Q = 6. The possibility of a fluctuating phase in unstrained Sn/Si(111) is discussed.
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