This paper addresses two important aspects of anti-windup (AW) designs, namely the parametrization of linear AW compensators, and the role of artificial nonlinearity (AN) in the design of AW compensators for multivariable systems. For the first issue, a simple parametrization is given using the classical feedback structure in the framework of constrained unity-feedback multivariable control systems. For the second issue, two existing AN designs for coordinating plant inputs whenever one plant input enters saturation are reviewed. A comparative simulation study illustrates that the conditioning technique, enhanced by optimal AN design, gives the best tracking performance among different existing methods.