Achieving low-latency consensus in geographically distributed systems remains a key challenge for blockchain and distributed database applications. To this end, there has been significant recent interest in State-Machine-Replication (SMR) protocols that achieve 2-round finality under the assumption that $5f+1\leq n$, where $n$ is the number of processors and $f$ bounds the number of processors that may exhibit Byzantine faults. In these protocols, instructions are organised into views, each led by a different designated leader, and 2-round finality means that a leader's proposal can be finalised after just a single round of voting, meaning two rounds overall (one round for the proposal and one for voting). We introduce Minimmit, a Byzantine-fault-tolerant SMR protocol with lower latency than previous 2-round finality approaches. Our key insight is that view progression and transaction finality can operate on different quorum thresholds without compromising safety or liveness. Experiments simulating a globally distributed network of 50 processors, uniformly assigned across ten virtual regions, show that the approach leads to a 23.1% reduction in view latency and a 10.7% reduction in transaction latency compared to the state-of-the-art.