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Aiming at a complete classification of unitary N=2 minimal models (where theassumption of space-time supersymmetry has been dropped), it is shown that eachmodular invariant candidate of a partition function for such a theory is indeedthe partition function of a minimal model. A family of models constructed viaorbifoldings of either the diagonal model or of the space-time supersymmetricexceptional models demonstrates that there exists a unitary N=2 minimal modelfor every one of the allowed partition functions in the list obtained fromGannon's work.  Kreuzer and Schellekens' conjecture that all simple current invariants can beobtained as orbifolds of the diagonal model, even when the extra assumption ofhigher-genus modular invariance is dropped, is confirmed in the case of theunitary N=2 minimal models by simple counting arguments.

On the complete classification of the unitary N=2 minimal superconformal field theories