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We consider the reduced model for thin-film devices in stationary micromagnetics proposed in [DeSimone, Kohn, Müller, Otto, Schäfer 2001]. In the case of soft/i> material, one of the energy contributions is negligible, and the problem becomes degenerate. The analysis and the numerical scheme recently developed in [Ferraz-Leite, Melenk, Praetorius 2011] are not satisfactory in this case. In the present work, we overcome the degeneracy and extend the numerical scheme by introducing a stabilizing energy term. Convergence of the method is established and a numerical experiment concludes the paper.