Maize with a modified amino acid profile, i.e. greater amounts of lysine and tryptophan than normal, is known as ‘quality protein maize’ (QPM). The objective of this work was to find the best combination of extrusion process variables to produce QPM flour for making tortillas. QPM grits were mixed with lime and water and had a moisture content of 28%. The single screw extruder operation conditions were selected from factorial combination of three process variables: extrusion temperature (ET, 70–100 °C), lime concentration (LC, 0.1–0.3% of the maize weight) and screw velocity (SV, 80–250 rpm). Response surface methodology was used as an optimization technique. In vitro protein digestibility (PD); total colour difference (ΔE) of the flours, and tortilla puffing (TP) were chosen as response variables. A graphical method was used to obtain maximum PD, TP and minimum ΔE. The optimum combination of process variables was: ET = 85 °C/LC = 0.21%(w/w)/SV = 240 rpm. Tortillas from QPM flour had similar chemical composition, physicochemical and sensory properties to tortillas from commercial nixtamalized maize flour; however, the former had the highest (P ≤ 0.05) available lysine content and were therefore better nutritionally.