In order to make a decision in the face of multiple objectives it is necessary to know the relative importance of the different objectives. Yet, it is often very difficult to specify a set of precise weights before possible alternatives solutions are known. In this paper, we present an interactive, iterative method for arriving at an acceptable solution. The decision maker gradually discerns what is achievable and adjusts his aspirations and (implicitly) the specification of weights and trade-offs between his objectives, in the light of what he learns. To aid the decision maker's cognition and to allow him to express his wishes in a natural way, we employ an intuitive interface, based on the parallel coordinates method of displaying and specifying points in multidimensional space.