Blind signatures play a central role in applications such as e-cash and e-voting systems. The notion of partially blind signature is a more applicable variant such that the part of the message contains some common information pre-agreed by the signer and the signature requester in an unblinded form. In this paper, we propose two efficient partially blind signatures with provable security in the random oracle model. The former is based on witness indistinguishable (WI) signatures. Compared with the state-of-the-art construction due to Abe and Fujisaki [1], our scheme is 25% more efficient while enjoys the same level of security. The latter is a partially blind Schnorr signature without relying on witness indistinguishability. It enjoys the same level of security and efficiency as the underlying blind signature.