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Stability of the all-pole model in conventional, unconstrained linear prediction with the autocorrelation criterion is well known. By exerting constraints to the optimisation problem it is possible to define models of order m + l with m parameters. However, traditionally constraints have led to models whose stability is not guaranteed. In this paper, we discuss constrained linear predictive models where the constraint is one-dimensional (l = 1) and derive stability criteria for these models.