Optimistic concurrency control (OCC) can exploit the strengths of parallel hardware to provide excellent performance for uncontended transactions, and is popular in high-performance in-memory databases and transactional systems. But at high contention levels, OCC is susceptible to frequent aborts, leading to wasted work and degraded performance. Contention managers, mixed optimistic/pessimistic concurrency control algorithms, and novel optimistic-inspired concurrency control algorithms, such as TicToc, aim to address this problem, but these mechanisms introduce sometimes-high overheads of their own. We show that in real-world benchmarks, traditional OCC can outperform these alternative mechanisms by simply adding fine-grained version timestamps (using different timestamps for disjoint components of each record). With fine-grained timestamps, OCC gets 1.14x TicToc's throughput in TPC-C at 128 cores (previous work reported TicToc having 1.8x higher throughput than OCC at 80 hyperthreads). Our study shows that timestamp granularity has a greater impact than previously thought on the performance of transaction processing systems, and should not be overlooked in the push for faster concurrency control schemes.