Hana Rudova. Constraints with variables' annotations. Technical Report FIMU-RS-98-04, 14 pages. Faculty of Informatics, Masaryk University, May 1998. This is an extended version of the paper accepted for presentation at ECAI-98. 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.