This paper addresses the vertical partitioning of a set of logical records or a relation into fragments. The rationale behind vertical partitioning is to produce fragments, groups of attribute columns, that “closely match” the requirements of transactions. Vertical partitioning is applied in three contexts: a database stored on devices of a single type, a database stored in different memory levels, and a distributed database. In a two-level memory hierarchy, most transactions should be processed using the fragments in primary memory. In distributed databases, fragment allocation should maximize the amount of local transaction processing. Fragments may be nonoverlapping or overlapping. A two-phase approach for the determination of fragments is proposed; in the first phase, the design is driven by empirical objective functions which do not require specific cost information. The second phase performs cost optimization by incorporating the knowledge of a specific application environment. The algorithms presented in this paper have been implemented, and examples of their actual use are shown.