Many distributed applications require transactions. However, transactional protocols that require strong synchronization are costly in large scale environments. Two properties help with scalability of a transactional system: genuine partial replication (GPR), which leverages the intrinsic parallelism of a workload, and snapshot isolation (SI), which decreases the need for synchronization. We show that, under standard assumptions (data store accesses are not known in advance, and transactions may access arbitrary objects in the data store), it is impossible to have both SI and GPR. To circumvent this impossibility, we propose a weaker consistency criterion, called Non-monotonic Snapshot Isolation (NMSI). NMSI retains the most important properties of SI, i.e., read-only transactions always commit, and two write-conflicting updates do not both commit. We present a GPR protocol that ensures NMSI, and has lower message cost (i.e., it contacts fewer replicas and/or commits faster) than previous approaches.