It is well recognized that data cubes often produce huge outputs. Several efforts were devoted to this problem through Constrained Cubes allowing the user to focus on a particular set of interesting tuples. In this paper, we investigate reduced representations for the Constrained Cube (e.g., Constrained Closed Cube and Constrained Quotient Cube). That is why we introduce a new and concise representation of data cubes: the Constrained Closed Non Derivable Data Cube (CCND-Cube). The latter captures all the tuples of a data cube fulfilling a combination of monotone/anti-monotone constraints. It can be represented in a very compact way in order to optimize both computation time and required storage space. The results of our experiments confirm the relevance of our proposal