The weak instance model is a framework to consider the relations in a database as a whole, regardless of the way attributes are grouped in the individual relations. Queries and updates can be performed involving any set of attributes. The management of updates is based on a lattice structure on the set of legal states, and inconsistencies and ambiguities can arise. In the general case, the test for consistency and determinism may involve the whole database. In this paper it is shown how, for the highly signi cant class of independent schemes, updates can be handled e ciently, considering only the relevant portion of the database. Key words. Relational databases, weak instance model, lattice on database states, update operations, chase procedure, optimization AMS subject classi cations. 68P15, 68Q25, 05A05