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This paper discusses the problem of estimating aspiration or reference levels in criteria space from choices between alternatives characterized by multiple criteria. Several methods for such estimations are developed and compared, taking into account both solution quality and computational efficiency. Methods based on mixed integer linear programming, which provide optimal solutions, require inacceptable computing times for application in interactive systems. An alternative method, based on a direct search algorithm, is shown to be an effective way of generating high quality estimates with small computational effort.