Identity-Based Encryption (IBE) offers an interesting alternative to PKI-enabled encryption as it eliminates the need for digital certificates. While revocation has been thoroughly studied in PKIs, few revocation mechanisms are known in the IBE setting. Until quite recently, the most convenient one was to augment identities with period numbers at encryption. All non-revoked receivers were thus forced to obtain a new decryption key at discrete time intervals, which places a significant burden on the authority. A more efficient method was suggested by Boldyreva, Goyal and Kumar at CCS'08. In their revocable IBE scheme, key updates have logarithmic (instead of linear in the original method) complexity for the trusted authority. Unfortunately, security could only be proved in the selective-ID setting where adversaries have to declare which identity will be their prey at the very beginning of the attack game. In this work, we describe an adaptive-ID secure revocable IBE scheme and thus solve a problem left open by Boldyreva et al..