In this study, a new reconstruction approach is proposed for the line segments that are nearly-aligned(<= 10 degrees) with the epipolar line. The method manipulates the redundancy inherent in line pair-relations to generate artificial 3D point entities and utilize those entities during the estimation process to improve the height values of the reconstructed line segments. The best point entities for the reconstruction are selected based on a newly proposed weight function. To test the performance of the proposed approach, we selected three test patches over a built up area of the city of Vaihingen-Germany. Based on the results, the proposed approach produced highly promising reconstruction results for the line segments that are nearly-aligned with the epipolar line.