We examine whether the flow tube along the edge of a coronal streamer supports standing shocks in the inner slow wind by solving an isothermal wind model in terms of the Lambert W function.It is shown that solutions with standing shocks do exist and they exist in a broad area in the parameter space characterizing the wind temperature and flow tube.In particular,streamers with cusps located at a heliocentric distance(>~)3.2R⊙ can readily support discontinuous slow winds with temperatures barely higher than 1 MK.