Byzantine Agreement requires a set of nodes in a distributed system to agree on the message of a sender despite the presence of arbitrarily faulty nodes. Solutions for this problem are generally divided into two classes: authenticated protocols and non-authenticated protocols. In the former class, all messages are (digitally) signed and can be assigned to their respective signers, while in the latter no messages are signed. Authenticated protocols can tolerate an arbitrary number of faults, while non-authenticated protocols require more than two thirds of the nodes to be correct. In this paper, we investigate the fault tolerance of protocols that require signatures in a certain number of communication rounds only. We show that a protocol that is to tolerate one half of the nodes as faulty needs only few authenticated rounds (logarithmic in the number of nodes), while tolerating more faults requires about two authenticated rounds per additional faulty node.