Since the two-view orthographic representation of a 3D object is ambiguous, it requires a numerous amount of combinatorial searches in the process of reconstruction. This paper presents an efficient algorithm for reconstructing polyhedral 3D objects from two-view drawings. The main feature of the algorithm is to improve the reconstruction process speed. First, the partially constructed objects are reconstructed from the restricted candidate faces corresponding to each area on the two-view drawings. Then the complete objects are obtained from the partially constructed objects by adding perpendicular faces with geometrical validity. By limiting the number of candidate faces corresponding to areas only, the combinatorial search space can be considerably reduced. In addition, the reconstruction finds the most plausible 3D object that human observers are most likely to select first among the given multiple solutions. Several examples from a working implementation are given to demonstrate the completeness of the algorithm.