This paper proposes methods and a technique for converting incorrect or ambiguous orthographic projections to solid models. First two methods are proposed for handling incorrect draftings that have redundant lines or missing lines, and the third one is a technique to reduce the number of candidates from ambiguous draftings. The first method is for detecting inconsistent lines, which must not appear in orthographic projections. For generating solid models, the system searches for 2D lines that cause inconsistency, and automatically removes them from the original draftings. Such inconsistent lines can be efficiently detected using nogood environments maintained by an ATMS. The second method is for the recovery of missing lines. If the proper wireframe model cannot be obtained from orthographic projections, it is impossible to search for solid shapes that match the draftings. In such a case, candidate missing lines are added in draftings to satisfy the condition that all 2D lines correspond to at least one edge in a 3D model. Boolean equations are re-calculated based on the modified draftings, and are solved using ATMS. Finally, to reduce the number of candidate solids that are generated from ambiguous orthographic projections, we use a technique to introduce additional constraints of cells. Our experiments show that our methods and technique are efficient enough for practical use. We observe that an ATMS mechanism is adequate to solving these equations, because sufficient constraints are derived by examining relationships among 3D models and projections, and described as Boolean equations.