The article is concerned with the proposal of a new approach of conceptual database design, called evolving conceptual database design, which exploits the structure for the preservation of database classes/concepts within the design. In order to discuss the opportunity to take into consideration this approach, the structure is constructed starting from a database conceptual graph. The leaves of the structure are mapped to a logical/object database graph. Horizontal steps of constructive logical database design extend the model. The computational costs required to design the structure for the preservation of database classes/concepts, as well as the qualitative/conceptual costs of the logical models resulting from the constructive design, are discussed.