In order to scale to large multiprocessors or clusters, transactional memories must reduce reliance on synchronisation. Therefore, we consider two favorable formal properties, namely Snapshot Isolation (SI, by which read-only transactions commit without synchronisation), and Genuine Partial Replication (GPR, by which a processor synchronises for a transaction only if it maintains a copy of some data item accessed by that transaction). We show that, unless the read-set of every transaction is known in advance, the combination of SI+GPR is impossible. To circumvent this impossibility result, we propose to weaken SI such that snapshots are allowed to be non-monotonic.