In Part I, the authors utilized frequency domain techniques to obtain low-order sensitivity models M of m-input, linear, constant, nth-order dynamic systems. The purpose of this paper is to develop a constructive approach for determining the minimal order (ρ) of M. Forsingle-inputsystems it is demonstrated that ρ = n and fornormalsystems ρ = inn. For general systems, tight upper and lower bounds on ρ are provided. These bounds are stated in terms of the system structural properties. Procedures for synthesizing the minimal-order sensitivity models are mentioned. Examples motivate and illustrate both the key ideas and applications of the results.