chipping transactions into pieces is good for performance but may lead to non-serializable executions. many researches 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 -has only degree 2 and degree 3 consistency options offered by the vast majority of conventional database systems; and - knows the set of transactions that may run during a certain interval (users are likely to have such knowledge for online real-time transactional applications) Given this information our algorithm find the finest partitioning of a set of transaction transet with the following property: if the partitioned transactions execute serializabily, rhen transet execute serializabily. this permits users to obtain more concurrency while preserving correctness. besides obtaining more inter-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 transaction in the interval, e is the number od edges in the conflict graph among the transaction, in is the maximum number of accesses of any transaction. this makes it feasible to add as a tuning knob to practical systems.