We present the first traitor tracing scheme with efficient black-box traitor tracing in which the ratio of the ciphertext and plaintext lengths (the transmission rate) is asymptotically 1, which is optimal. Previous constructions in thissetting either obtained constant (but not optimal) transmission rate [KY02b], or did not support black-box tracing [CPP05]. Our treatment improves the standard modeling of black-box tracing by additionally accounting for pirate strategies that attempt to escape tracing by purposedly rendering the transmitted content at lower quality. Our construction relies on the decisional bilinear Diffie-Hellman assumption, and attains the same features of public traceability as (a repaired variant of) [CPP05], which is less efficient and requires non-standard assumptions for bilinear groups.