This paper first extends the result of Blakley and Kabatianski [3] to general non-perfect SSS using information-theoretic arguments. Furthermore, we refine Okada and Kurosawa's lower bound [12] into a more precise information-theoretic characterization of non-perfect secret sharing idealness. We establish that in the light of this generalization. ideal schemes do not always have a matroidal morphology. As an illustration of this result, we design an ad-hoc ideal non-perfect scheme and analyze it in the last section.