The dependence of K⁺ production on the nuclear equation of state is investigated in heavy ion collisions. An increase in the excitation function of K⁺ multiplicities obtained in heavy (Au+Au) over light (C+C) systems when going far below the threshold which has been observed by the KaoS Collaboration, strongly favours a soft equation of state. This observation holds despite the influence of an in-medium kaon potential predicted by effective chiral models which is necessary to reproduce the experimental K⁺ yields. Phase space effects are discussed with respect to the K⁺ excitation function.