COOL (Chen'21) is an error-free and deterministic Byzantine agreement protocol that achieves consensus on an $\ell$-bit message with a communication complexity of $O(\max\{n\ell, n t \log t \})$ bits in four phases, given $n\geq 3t + 1$, for a network of $n$ nodes, where up to $t$ nodes may be dishonest. In this work we show that COOL can be optimized by reducing one communication round. The new protocol is called OciorCOOL. Additionally, building on OciorCOOL, we design an optimal reliable broadcast protocol that requires only six communication rounds.