Bounds on differences are widely used in AI to model binary constraints regarding different dimensions, such as time, space, costs, calories, etc. Representing and reasoning with them is an important task in several areas such as knowledge representation, scheduling and planning. Researchers are increasingly focusing on the treatment of fuzzy or probabilistic constraints, to deal with preferences and/or uncertainty. Current approaches to constraints with preferences focus on the evaluation of the optimal (i.e., with highest preference) solutions for the set of constraints and propose a wide range of alternative operators to combine preferences within constraint propagation. However, in decision support tasks, finding a specific (though optimal) solution is not the main goal, but rather it is more important to identify the "space of solutions" (i.e., the minimal network) with their preferences, and to provide users with query answering mechanisms to explore it. We propose the first approach that addresses such a need by (i) supporting user-defined layered scales of preferences (e.g., Low, Medium, High, Very High), (ii) proposing a family of extensions of bounds on differences constraints to deal with such layered preferences, (iii) defining a family of reasoning algorithms to evaluate the minimal network, which is parametric with respect to the basic operations to combine preferences (and the scale of preferences), and (iv) providing suitable query-answering facilities. The properties of the family of approaches are also analyzed.