The article introduces the new computer program *SHELXT*, which employs a dual-space algorithm to solve the phase problem for single-crystal reflection data expanded to the space group *P1*. The program accounts for missing data and extends resolution if necessary. It tests all space groups in the specified Laue group to find those consistent with the *P1* phases. After applying origin shifts and space-group symmetry, the solutions undergo further dual-space recycling, peak search, and electron density summation. Elements are assigned to maximize integrated peak densities, and isotropic refinement is performed for non-centrosymmetric space groups, followed by Flack parameter calculation and structure inversion if appropriate. *SHELXT* has a high success rate in solving thousands of structures and is optimized for multiprocessor computers, but it is not suitable for severely disordered or twinned structures. The article also discusses the dual-space iteration starting from a Patterson superposition, the random omit procedure, and the process of assigning chemical elements to electron-density peaks. Examples are provided to illustrate the program's effectiveness in solving crystal structures.The article introduces the new computer program *SHELXT*, which employs a dual-space algorithm to solve the phase problem for single-crystal reflection data expanded to the space group *P1*. The program accounts for missing data and extends resolution if necessary. It tests all space groups in the specified Laue group to find those consistent with the *P1* phases. After applying origin shifts and space-group symmetry, the solutions undergo further dual-space recycling, peak search, and electron density summation. Elements are assigned to maximize integrated peak densities, and isotropic refinement is performed for non-centrosymmetric space groups, followed by Flack parameter calculation and structure inversion if appropriate. *SHELXT* has a high success rate in solving thousands of structures and is optimized for multiprocessor computers, but it is not suitable for severely disordered or twinned structures. The article also discusses the dual-space iteration starting from a Patterson superposition, the random omit procedure, and the process of assigning chemical elements to electron-density peaks. Examples are provided to illustrate the program's effectiveness in solving crystal structures.