In this paper, we design and analyze some new and practical (selectively) convertible undeniable signature (SCUS) schemes in both random oracle and standard model, which enjoy several merits over existing schemes in the literature. In particular, we design the first practical RSA-based SCUS schemes secure in the standard model. On the path, we also introduce two moduli RSA assumptions, including the strong twin RSA assumption, which is the RSA symmetry of the strong twin Diffie-Hellman assumption (Eurocrypt'08).