Reductions of (2+1)-dimensional integrable systems via mixed potential-eigenfunction constraints

New types of reductions of (2+1)-dimensional integrable systems which are associated with mixed potential-eigenfunction constraints are discussed. Necessary and sufficient conditions for the admissibility of such constraints are presented. Classification results for integrable equations will be used for applying these conditions. Several typical examples are considered, including the KP, mKP, (2+1)-dimensional Savada-Kotera-Kaup-Kupershmidt, Harry Dym and Nizhnik-Veselov-Novikov equations.