Many compiler optimization techniques depend on the ability to calculate the number of integer values that satisfy a given set of linear constraints. This count is a function of the symbolic parameters that typically appear in the constraints and it is known as the enumeration of a parametric polytope. In an extended problem, some of the variables that appear in the constraints may be existentially quantified and then the enumerated set corresponds to the projection of the integer points in a parametric polytope. We refer to this problem as the enumeration of the integer projection of a parametric polytope. This paper shows how the enumeration of the integer projection of parametric polytopes can be reduced to the enumeration of parametric polytopes. Two approaches are described and experimentally compared. Di?erences are small, but both methods can solve problems that previously were considered very difficult to solve analytically.