The greedy method is a well-known approach for problem solving directed mainly at the solution of optimization problems. Leading theoretical frameworks dealing with the optimality of greedy solutions (e.g., the matroid and greedoid theories) tacitly assume that the greedy algorithm is always guided by the cost function to be optimized, namely, it builds a solution by adding, in each step, an element that contributes the most to the value of the cost function. This paper studies a class of problems for which this type of a greedy algorithm does not optimize the given cost function, but for which there exists a secondary objective function, called a greedy rule, such that applying the greedy algorithm to the secondary objective function yields a solution which is optimal with respect to the original cost function. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.