It is often possible to improve a concurrent system's performance by leveraging the semantics of its datatypes. We build a new software transactional memory (STM) around this observation. A conventional STM tracks read-and writesets of memory words; even simple operations can generate large sets. Our STM, which we call STO, tracks abstract operations on transactional datatypes instead. Parts of the transactional commit protocol are delegated to these datatypes' implementations, which can use datatype semantics, and new commit protocol features, to reduce bookkeeping, limit false conflicts, and implement efficient concurrency control. We test these ideas on the STAMP benchmark suite for STM applications and on our own prior work, the Silo high-performance in-memory database, observing large performance improvements in both systems.