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As object-relational databases (ORDBs) become popular in the industry, it is important for database designers to produce database schemes with good properties in these new kinds of databases. One distinguishing feature of an ORDB is that its tables may not be in first normal form. Hence, ORDBs may contain nested relations along with other collection types. To help the design process of an ORDB, several normal forms for nested relations have recently been defined, and some of them are called nested normal forms. In this paper, we investigate four nested normal forms, which are NNF 20, NNF 21, NNF 23, and NNF 25, with respect to generalizing 4NF and BCNF, reducing redundant data values, and design flexibility. Another major contribution of this paper is that we provide an improved algorithm that generates nested relation schemes in NNF 2 from an $ database scheme, which is the most general type of acyclic database schemes. After presenting the algorithm for NNF 20, the algorithms of all of the four nested normal forms and the nested database schemes that they generate are compared. We discovered that when the given set of MVDs is not conflict-free, NNF 20 is inferior to the other three nested normal forms in reducing redundant data values. However, in all of the other cases considered in this paper, NNF 20 is at least as good as all of the other three nested normal forms.