In the present work, we propose a method to generate high-quality optical vortices with a reduced number of phase levels by using multilevel vortex-producing lenses (VPLs). The VPL is implemented in a liquid-crystal spatial light modulator with limited capacity to project phase levels. The proposed method significantly improves the quality of the optical vortex obtained by employing spiral phase plates with the same number of phase levels. Simulations and experimental results confirming the effectiveness of the method are presented.