Unauthenticated Byzantine consensus protocols achieve optimal failure resilience while relying only on authenticated point-to-point channels, not authenticated messages. They are an attractive building block for blockchains that do not mandate symmetric trust assumptions as well as for future post-quantum settings. We consider unauthenticated Byzantine consensus in partially synchronous networks and focus on optimizing its good-case latency - the worst-case time for correct processes to reach a decision under favorable conditions. A recently proposed ForgetIT protocol achieves an optimal good-case latency of 3 message delays but employs a highly complex design. We show that this complexity is unnecessary. To this end, we present Fast TetraBFT - an unauthenticated Byzantine consensus protocol that achieves optimal good-case latency by augmenting an existing TetraBFT protocol with a simple fast-path wrapper. Our solution lowers the good-case latency of TetraBFT from 5 to 3 message delays while preserving its bounded space requirements and low communication complexity.