The stability of parametrically excited standing waves in large-aspect-ratio systems is investigated for small driving. Their phase diffusion equation is derived. It is found that for small group velocity of the underlying travelling waves the Eckhaus-stable band of wave numbers can split up into two subbands which are separated by a region of unstable wave numbers. This gives rise to solutions with stable wave-number kinks which bridge the unstable regime between the subbands. The kinks are approximately described by a Ginzburg-Landau equation for a conserved order parameter. For other parameter values the transition to an equivalent of the Benjamin-Feir instability can be controlled by the driving amplitude.