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We address the recently recognized privatization problem in software transactional memory (STM) runtimes, and introduce the notion of partially visible reads (PVRs) to heuristically reduce the overhead of transparent privatization. Specifically, PVRs avoid the need for a "privatization fence" in the absence of conflict with concurrent readers. We present several techniques to trade off the cost of enforcing partial visibility with the precision of conflict detection. We also consider certain special-case variants of our approach, e.g., for predominantly read-only workloads. We compare our implementations to prior techniques on a multicore Niagara1 system using a variety of artificial workloads. Our results suggest that while no one technique performs best in all cases, a dynamic hybrid of PVRs and strict in-order commits is stable and reasonably fast across a wide range of load parameters. At the same time, the remaining overheads are high enough to suggest the need for programming model or architectural support.