Cordial Miners are a family of efficient Byzantine Atomic Broadcast protocols, with instances for asynchrony and eventual synchrony. They improve the latency of state-of-the-art DAG-based protocols by almost $2\times$ by forgoing reliable broadcast as a building block. Rather, Cordial Miners use the blocklace -- a partially-ordered generalization of the blockchain data structure -- for all algorithmic aspects of consensus: Dissemination, equivocation-exclusion, and ordering.