The usefulness of fully performed constant-momentum-transfer-averaging (CMTA) in low-energy electron diffraction (LEED) has been demonstrated for a single-domain Si(111)4×1-In surface. In the fully performed CMTA, thousands of I(V) curves were measured for the single-domain Si(111)4×1-In surface and CMTA intensity profiles were obtained for more than three hundred reciprocal rods in order to directly reconstruct three dimensional (3D) atomic positions of the surface. In the direct reconstruction, the minimum function method, a standard method in X-ray crystallography of the Patterson function analysis, was used. The 3D Si positions so obtained were in excellent agreement with the known heavily-reconstructed surface Si positions of 4×1. Indium atoms were not ‘ visible’ in the present case due to large thermal vibration amplitude of indium atoms for the room-temperature sample, which is not an inherent shortcoming of the fully performed CMTA method. [DOI: 10.1380/ejssnt.2006.661]