We present an algorithm to construct a tight bounding polyhedron for a recursive procedural model. We first use an iterated function system (IFS) to represent the extent of the procedural model. Then we present a novel algorithm that expresses the IFS-bounding problem as a set of linear constraints on a linear objective function, which can then be solved via standard techniques for linear convex optimization. As such, our algorithm is guaranteed to find the recursively optimal bounding polyhedron, if it exists. Finally, we demonstrate examples of this algorithm on two and three dimensional recursive procedural models.