Experimental high-quality optical vortices of different topological charges are generated by using a vortex producing lens with two phase levels. In our setup, the lens is displayed on a liquid-crystal spatial light modulator that only attains phase modulation of around 1.2π. This achievement opens the real possibility of creating high-quality optical vortices with devices of very low phase modulation capacity. The experimental setup is fully described, and the considerations to set the optimal parameters to obtain high-quality optical vortices are discussed and experimentally established. The phase and intensity of the optical vortices are recovered. The phase is obtained through a phase-shifting method that is directly programmed onto the modulator avoiding any class of mechanical displacement.