Tammisola et al (2012 J. Fluid Mech. 713 632-58) have observed a counter-intuitive destabilizing effect of the surface tension in planar wakes by means of a global linear analysis. In the present study, we conduct direct numerical simulation (DNS) of wakes of two immiscible fluids. The numerical scheme is based on a level set approach to track the interface position. We simulate both sinuous and varicose perturbations of wake flows. DNS confirms a destabilization on the sinuous perturbations in presence of a moderate amount of the surface tension, while wakes are stabilized when the surface tension is further increased. Varicose perturbations present in contrast an intermittent low-amplitude oscillatory regime which does not significantly affect the position of the interface.