This brief paper provides a comparison of methods for enclosing a given zonotope within another of lower complexity, commonly called order reduction. These techniques are essential for maintaining efficiency in recursive computations with zonotopes and are widely used in set-based estimation, hybrid systems verification, and fault detection. We first review existing methods and provide a new theoretical analysis of the method recently introduced by Scott et al. (2016). We then compare methods in terms of computational cost and overestimation error, and investigate the effects of zonotope dimension, initial order, and reduced order on these metrics. These results provide valuable guidance for the design of robust estimation and control algorithms that more effectively balance accuracy with computational cost. (C) 2018 Elsevier Ltd. All rights reserved.