In this study, a new 3D reconstruction approach for line segments from stereo images is proposed which covers the case that the image lines are nearly-aligned (<= 10 degrees) with the epipolar line. The method manipulates the redundancy inherent in line pair-relations to generate artificial 3D points and utilizes those entities during the estimation process to improve the reconstruction of the line segments. The best points 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. The proposed approach produced a highly promising reconstruction performance for line segments that are nearly aligned with the epipolar line.