Distributed storage systems run transactions across machines to ensure serializability. Traditional protocols for distributed transactions are based on two-phase locking (2PL) or optimistic concurrency control (OCC). 2PL serializes transactions as soon as they conflict and OCC resorts to aborts, leaving many opportunities for concurrency on the table. This paper presents ROCOCO, a novel concurrency control protocol for distributed transactions that outperforms 2PL and OCC by allowing more concurrency. ROCOCO executes a transaction as a collection of atomic pieces, each of which commonly involves only a single server. Servers first track dependencies between concurrent transactions without actually executing them. At commit time, a transaction's dependency information is sent to all servers so they can re-order conflicting pieces and execute them in a serializable order. We compare ROCOCO to OCC and 2PL using a scaled TPC-C benchmark. ROCOCO outperforms 2PL and OCC in workloads with varying degrees of contention. When the contention is high, ROCOCO's throughput is 130% and 347% higher than that of 2PL and OCC.