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We establish a robust schema design framework for data with missing values. The framework is based on the new notion of an embedded functional dependency, which is independent of the interpretation of missing values, able to express completeness and integrity requirements on application data, and capable of capturing many redundant data value occurrences. We establish axiomatic, algorithmic, and logical foundations for reasoning about embedded functional dependencies. These foundations allow us to establish generalizations of Boyce-Codd and Third normal forms that do not permit any redundancy in any future application data, or minimize their redundancy across dependency-preserving decompositions, respectively. We show how to transform any given schema into application schemata that meet given completeness and integrity requirements and the conditions of the generalized normal forms. Data over those application schemata are therefore fit for purpose by design. Extensive experiments with benchmark schemata and data illustrate our framework, and the effiectiveness and efficiency of our algorithms, but also provide quantified insight into database schema design trade-offs. [ABSTRACT FROM AUTHOR]