This paper generalizes the results obtained by the authors in [1] and presents new results on the construction of proper controllers for linear multivariable regulators. These results appear to lead to efficient computational methods that do not involve Smith forms nor the order relations used in [1] to construct proper controllers. The methods are based on the recently developed theory of Λ-generalized polynomials [2]. We discuss several new computational algorithms and how they can be applied to the regulator problem.