In this paper the problem of constructing the minimum l(1), uncertainty model containing a finite set of assigned models is addressed. This problem is relevant to l(1) robust control design techniques, in order to minimize the size of the uncertainty set associated to the nominal plant. The problem is formulated as a (conditional) Chebyshev center problem and an algorithm for its Solution is proposed. The algorithm converges in a finite number of steps showing computational efficiency for large size problems. (C) 2008 Elsevier Ltd. All rights reserved.