We propose a new notion of short identity-based signature scheme. We argue that the identity-based environment is essential in some scenarios. The notion of short identity-based signature schemes can be viewed as identity-based (partial) message recovery signatures. Signature schemes with message recovery has been extensively studied in the literature. This problem is somewhat related to the problem of signing short messages using a scheme that minimizes the total length of the original message and the appended signature. In this paper, firstly, we revisit this notion and propose an identity-based message recovery signature scheme. Our scheme can be regarded as the identity based version of Abe-Okamoto’s scheme . Then, we extend our scheme to achieve an identity-based partial message recovery signature scheme. In this scheme, the signature is appended to a truncated message and the discarded bytes are recovered by the verification algorithm. This is to answer the limitation of signature schemes with message recovery that usually deal with messages of fixed length. This paper opens a new research area, namely how to shorten identity based signatures, in contrast to proposing a short signature scheme. We present this novel notion together with two concrete schemes based on bilinear pairings.