Objects and scenes encountered in close-range photogrammetry, vision metrology and virtual reality applica-tions may often be adequately modeled as specific combinations of straight lines and/or line-defined planes. The descriptive power of lines for 3D object reconstruction and their suitability for automatic extraction justify the strong interest in line-based approaches introducing straight linear features as primitives in fundamental photogrammetric tasks. Notwithstanding the suitability of single image line-based techniques for several cali-bration/orientation and reconstruction problems, stereopairs provide a higher potential. Here, the question of relative orientation of the stereopair based on straight lines is addressed as a geometrically powerful tool also allowing partial 3D reconstruction. Investigation of the problem showed that solution minimally requires a constraint of four coplanar lines. Besides this “structural” constraint, however, additional constraints are ex-pected to further enhance the ground truth of 3D reconstruction. In this contribution, results from “ordinary” stereopairs are presented with combinations of constraints among planes. It is clearly shown that the overall shape reconstruction is significantly improved, in particular as regards unconstrained relative directions of 3D lines or object symmetries defined by line intersections. Futher possible contraints are also discussed. Such approaches allow to fully exploit the potential of the stereopair in line-photogrammetry instead of streotriplets usually required in this context.