Some of the solution properties of an nth order single input-output system with bounded control in which the coefficient of the highest order derivative is a small parameter ε are discussed. In particular, the reachable set from the origin for this system can be approximated to within O(ε), as ε → 0 by reachable sets constructed from either of two (n — l)-dimensional systems. These approximating systems arise in a natural way, the first by a natural partitioning of the original system matrix and the second by setting ε = 0. The results have particular significance in the case n = 3.