Plane-strain thermomechanical finite element model experiments of lithospheric extension are used to investigate the effects of strain softening in the frictional plastic regime on the asymmetry of extension. Strain softening is considered in cases where the crust is either strongly or weakly coupled to the mantle, and as the extension velocity varies from 0.3 to 30 cm/yr. In the absence of strain softening, extension is symmetric (SS mode). When strain softening takes the form of a reduction in the internal angle of friction with increasing strain, lithospheric extension may be asymmetric at a lithospheric scale (AA mode), or exhibit crustal asymmetry concomitant with mantle symmetry (AS mode). The different styles depend on the relative control of the system by the frictional plastic and ductile layers, which promote asymmetry and symmetry, respectively. High extension velocities and weak ductile crust-mantle coupling tend to suppress the fundamental asymmetry induced by frictional strain softening. This is because they, respectively, increase the effective strength of the lower lithosphere and decrease the control by frictional plasticity.