In this paper, we present two early stopping Byzantine agreement protocols in the authenticated setting against a corrupt minority \(t < n/2\) , where t represents the maximum number of malicious parties. Early stopping protocols ensure termination within a number of rounds determined solely by the actual number of malicious nodes f present during execution, irrespective of t. Our first protocol is deterministic and ensures early stopping termination in \( (d+5) \cdot (\lfloor f/d \rfloor +2)+2\) rounds, where d is a fixed constant. For example, for all \(d\ge 6\) , our protocol runs in at most \((1+\epsilon )\cdot f\) rounds (where \(0<\epsilon <1\) ), improving (for large f) upon the best previous early stopping deterministic broadcast protocol by Perry and Toueg [21], which terminates in \(min(2f+4,2t+2)\) rounds. Additionally, our second protocol is randomized, ensuring termination in an expected constant number of rounds and achieving early stopping in \((d+9) \cdot (\lfloor f/d \rfloor +1)+2\) rounds in the worst case. This marks a significant improvement over a similar result by Goldreich and Petrank. [15], which always requires an expected constant number of rounds and O(t) rounds in the worst case, i.e., does not have the early stopping property.