Two classes of methods for optimizing the profile of a sparse matrix are given. Profile storage is useful when the matrix is moderately sparse, or when the nonzero entries are near the main diagonal. The proposed methods in the first class are heuristic. Two version of this are: minimizing the grown of zeros in each step and minimizing a weighted measure of growth of non zeros. In the second class, the methods are based on exchanges of adjacent rows and adjacent columns to strictly improve the profile. A series of adjacent exchanges is made if that may yield an improvement at later steps. Numerical comparisons between the ordering strategies are given.