We studied influence of post-processing (annealing and stress-annealing) on domain wall dynamics in Fe-, Ni- and Co-based magnetic microwires with spontaneous and induced magnetic bistability. As-prepared Co-based microwires with low and negative magnetostriction present linear hysteresis loops. Magnetic bistability in Co-based microwires has been induced by annealing. Minimizing magnetoelastic anisotropy either by adjusting the chemical composition with a low magnetostriction coefficient or by heat treatment is an appropriate route for the domain wall dynamics optimization in magnetic microwires. Stress-annealing allows further improvement of domain wall velocity and hence is a promising method allowing optimization of the DW dynamics in magnetic microwires. The beneficial influence of stress-annealing on the DW dynamics is explained considering an increase in the volume of outer domain shell with transverse magnetization orientation in expense of decrease in the radius of the inner axially magnetized core. Such transverse magnetic anisotropy can affect the DW dynamics in similar way as the applied transverse magnetic field and hence is beneficial for the DW dynamics optimization. Thus, stress-annealing allows designing the magnetic anisotropy distribution more favorable for the DW dynamics improvement. Co-rich microwires with magnetic bistability induced by annealing present a considerable enhancement in the DW velocity upon applied tensile stress: exactly the opposite to the case of magnetic microwires with spontaneous magnetic bistability. Observed dependence has been explained considering decrease in the magnetostriction coefficient under effect of the applied stress. Display omitted •Rectangular hysteresis loops of annealed Co-rich microwires.•Tuning of hysteresis loops varying stress-annealing conditions.•Enhancement of domain wall velocity after annealing and stress-annealing.•Enhancement of domain wall velocity by applied stress in Co-rich microwires.•Modification of the magnetic anisotropy distribution by stress-annealing.