LetRbe a Marot ring whose regular ideals are finitely generated andDa Krull overring ofR. In this paper, we show that if reg-dimR≥ 2, then each regular ideal ofDis finitely generated and reg-dimD≥ 2. In particular, each regular ideal of a Krull overring of a Noetherijan ringRis finitely generated provided that (regular) Krull-dimensionR≥ 2. This is a generalization of the well-known fact that a Krull overring of a Noetherian domain with Krull-dimension ≥ 2 is also a Noetherian domain with Krull-dimension ≥ 2.