It is shown that random duty-cycle errors in quasi-phase-matching (QPM) nonlinear optical devices enhance the efficiency of processes far from the QPM peak. An analytical theory is shown to agree well with numerical solutions of second-harmonic generation (SHG) in disordered QPM gratings. The measured efficiency of 1550 nm band SHG in a periodically poled lithium niobate (PPLN) waveguide away from the QPM peak agrees with observations of domain disorder in a PPLN wafer by Zygo interferometry. If suppression of parasitic nonlinear interactions is important in a specific application of QPM devices, control of random duty-cycle errors is critical.