Designated verifier signature (DVS) allows a signer to convince a designated verifier that a signature is generated by the signer without letting the verifier transfer the conviction to others, while the public can still tell that the signature must be generated by one of them. Strong DVS (SDVS) strengthens the latter part by restricting the public from tellingwhether the signature is generated by one of them or by someone else. In this paper, we propose two new SDVS schemes. Compared with existing SDVS schemes, the first new scheme has almost the same signature size and meanwhile, is proven secure in the standardmodel,while the existing ones are secure in the random oracle model. It has tight security reduction to the DDH assumption and the security of the underlying pseudorandom functions. Our second new scheme is the first SDVS supporting non-delegatability, the notion ofwhich was introduced by Lipmaa,Wang and Bao in the context of DVS in ICALP 2005. The scheme is efficient and is provably secure in the random oracle model based on the discrete logarithm assumption and Gap Diffie–Hellman assumption.