Traitor tracing is an important tool to discourage defrauders from illegally broadcasting multimedia content. However, the main techniques consist in tracing the traitors from the pirate decoders they built from the secret keys of dishonest registered users: with either a black-box or a white-box tracing procedure on the pirate decoder, one hopes to trace back one of the traitors who registered in the system. But new techniques for pirates consist either in sending the ephemeral decryption keys to the decoders for real-time decryption, or in making the full content available on the web for later viewing. This way, the pirate does not send any personal information. In order to be able to trace the traitors, one should embed some information, or watermarks, in the multimedia content itself to make it specific to the registered users. This paper addresses this problem of tracing traitors from the decoded multimedia content or rebroadcasted keys, without increasing too much the bandwidth requirements. More precisely, we construct a message-traceable encryption scheme that has an optimal ciphertext rate, i.e. the ratio of global ciphertext length over message length is arbitrarily close to one.