Hana Rudova. Constraints with variables' annotations. In Henri Prade, editor, 13th European Conference on Artificial Intelligence Proceedings (ECAI-98), pages 261-262. John Wiley & Sons, Ltd., August 1998. Extended version of the paper is available as a technical report FIMU-RS-98-04. Abstract: Variables' annotations in over-constrained problems are proposed and described in order to express preferences for optimal solution selection using preferences on variables. The basic interpretation of variables' annotations is presented and correspondence with hierarchical CSP and possibilistic CSP is described. An algorithm for solving systems of constraints with variables' annotations using mappings to hierarchy is designed. The potential application areas are also mentioned.