Proxy signatures, introduced by Mambo, Usuda and Okamoto allow a designated person to sign on behalf of an original signer. This paper first presents two new types of digital proxy signatures called partial delegation with warrant and threshold delegation. Proxy signatures for partial delegation with warrant combines the benefit of Mambo's partial delegation and Neuman's delegation by warrant, and then in threshold delegation the proxy signer's power to sign messages is shared. Moreover, we also propose straightforward and concrete proxy signature schemes satisfying our conditions.