Direct numerical simulations were used to simulate plane channel and plane Poiseuille-Couette flows. For Poiseuille-Couette flow, the walls of the channel were moving with a specified velocity. This is equivalent to forcing a slip velocity at the wall of the channel, and such flow behaviour can be viewed as the effect due to an ultra-hydrophobic wall. It was found that the location of the zero Reynolds stress value shifted towards the wall moving in the streamwise direction. The near-wall eddies were found to be longer and weaker than for the plane-Poiseuille channel flow. It appears that such an eddy structure can lead to turbulence drag reduction.