2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106304We describe all real points of the parameter space of two-generator Kleinian groups with a parabolic generator, that is, we describe a certain two-dimensional slice through this space. In order to do this we gather together known discreteness criteria for two-generator groups and present them in the form of conditions on parameters. We complete the description by giving discreteness criteria for groups generated by a parabolic and a $π$-loxodromic elements whose commutator has real trace and present all orbifolds uniformized by such groups.21 pages, 10 figuresGroup Theory30F40 (primary); 20H10, 22E40, 57M60 (secondary)text