A problem-solving method for assignment problems and a corresponding expert system shell named COKE are presented and evaluated. The method consists of four main steps. Until all elements are assigned: (1) select an element to be assigned next, (2) propose a partner element for that element, (3) if new constraints are violated after the proposed step, try exchanging elements to remove or minimize the constraint violations from a local point of view, and (4) if the completed assignment still violates constraints, try exchanges to remove or minimize them from a global point of view and with more effort. Each step can take advantage of problem-specific knowledge. The evaluation with COKE shows that flexibility is of key importance in dealing with different kinds of assignment problems.>