Serializability is too strict a correctness criterion for several application domains, in particular where support for long-lasting transactions is required. This paper describes a generalized version of serializability called conditional conflict serializability (CCSR), which is built on a customized notion of conflict rather than the standard commutativity-based one. The actual customization of conflicts is carried out by applications that associate parameters with their read and write operations. The semantics of such parameters are user-defined, and can be chosen to suit various needs. CCSR can be enforced by means of two phase locking with parameterized locks. Transaction histories that are strict or rigorous modulo CCSR are defined, showing that a CCSR scheduler need not rely on compensating actions for recovery.