Two-phase-commit (2PC) has been widely adopted for distributed transaction processing, but it also jeopardizes throughput by introducing two rounds of network communications and two durable log writes to a transaction's critical path. Despite the various proposals that eliminate 2PC such as deterministic database and access localization, 2PC remains the de facto standard since the alternatives often lack generality (e.g., requiring workloads without branches based on query results). In this paper, we present Primo, a distributed transaction protocol that supports a more general set of workloads without 2PC. Primo features write-conflict-free concurrency control that guarantees once a transaction enters the commit phase, no concurrency conflict (e.g., deadlock) would occur when installing the write-set -- hence the prepare phase is no longer needed to account for any potential conflict from any partition. In addition, Primo further optimizes the transaction path using asynchronous group commit. With that, the durability delay is also taken off the transaction's critical path. Empirical results on Primo are encouraging -- in YCSB and TPC-C, Primo attains 1.42x to 8.25x higher throughput than state-of-the-art general protocols including Sundial and COCO, while having similar latency as COCO which also employs group commit.