Chopping transactions into pieces is good for performance but may lead to non-serializable executions. Many research ers have reacted to this fact by either inventing new concurrency control mechanisms, weakening serializability, or both. We adopt a different approach. We assume a user who l has only the degree 2 and degree 3 consistency options offered by the vast majority of conventions] database systems; and knows the set of transactions that may run during a certain interval (users are likely to Jrave such knowledge for online or real-time transactional applications). Given this information, our algorifhm finds the finest parfifioning of a set of transactions TranSet with the following property: if the partitioned transactions execute serializable, then TranSet executes serializable. This permits users to obtain more concurrency while preserving correctness. Besides obtaining more inter-transaction concurrency, chopping transactions in this way can enhance intra-transaction parallelism. The algorithm is inexpensive, running in O(n x (e + m)) time using a naive implementation where n is the number of concurrent transactions in fhe interval, e is the number of edges in the conflict graph among the transactions, and m is the maximum number of accesses of any transaction. This makes it feasible to add as a tuning knob to pracfical Systems.