We give a generic construction for universal designated-verifier signature schemes from a large class, C, of signature schemes. The resulting schemes are efficient and have two important properties. Firstly, they are provably DV-unforgeable, non-transferable and also non-delegatable. Secondly, the signer and the designated verifier can independently choose their cryptographic settings. We also propose a generic construction for identity-based signature schemes from any signature scheme in C and prove that the construction is secure against adaptive chosen message and identity attacks. We discuss possible extensions of our constructions to universal multi-designated-verifier signatures, hierarchical identity-based signatures, identity-based universal designated verifier signatures, and identity-based ring signatures from any signature in C.