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A model of the expansion of a plasma in a magnetic nozzle in the full magnetization limit is presented. The fully magnetized and the unmagnetized-ions limits are compared, recovering the whole range of variability in plasma properties, thrust, and plume efficiency, and revealing the differences in the physics of the two cases. The fully magnetized model is the natural limit of the general, 2D, two-fluid model of Ahedo and Merino [Phys. Plasmas 17, 073501 (2010)], and it is proposed as an analytical, conservative estimator of the propulsive figures of merit of partially magnetized plasma expansions in the near region of the magnetic nozzle.