In this paper we present the design and implementation of a Class Ordering System that is driven by a parameterized cost model. The parameters to the model assign weights to the edge types that describe the relationships between the classes in the graphical representation of the program. The nodes in the graph are classes and the edges express relationships between the classes. Previous research has included three or four edge types in the graph. However, to accommodate the full complement of C++ language constructs, which include template classes and functions and nested classes, we extend the graph to include six edge types. The parameters to the cost model can be tuned to remove certain types of edges in an attempt to reduce the cost of the testing effort or to reduce the cost of breaking cycles in the graph. Our case study indicates that inclusion of inheritance edges in cycle breaking considerations may reduce the number of edge removals by a factor of two or more.