This paper studies the problem of identifying a monotone Wiener system from observed, noiseless input-output signals. Specifically, we study identifiability of such systems, as well as the convergence properties of the recently introduced MINimal LIPschitz (MINLIP) estimator. This estimator finds a system with minimal complexity by exploiting ordering of the output samples. This makes the approach conceptual quite different from traditional identification schemes based on least squares, prediction errors, maximum likelihood or numerical projections. Sufficient conditions from which the result follows are given in terms of 'Rotational Complete Inputs (RCI)', a generalization of the notion of Persistency of Excitation (PE) as used for the study of linear identification methods. Finally, it is derived that a Gaussian i.i.d. sequence satisfies this RCI property, while any binary sequence does not. (C) 2014 Elsevier Ltd. All rights reserved.