Abstract: A design method is proposed that sequentially generates observation sites for the construction of a kriging predictive model. The objective of the construction is to allow a precise inversion of the system in the following sense: with any reachable target point T in the output space one wishes to be able to associate an input vector x_T such that the system response at x_T will be close to T (which requires that the model ensures a precise prediction of the response at x_T ). Intuitively, the observation sites should not be spread over the admissible input space, but should rather concentrate in areas such that, when mapped by the system, they cover the reachable output space. Two approaches are proposed that are shown on examples (one with five input and two outputs, derived from a problem in oil industry) to give satisfactory results. They are based on the maximization of a measure of dispersion of the observations in the output space and can cope with the presence of observation errors, a rather typical situation for experimentation with real physical systems.