Researchers and practitioners advocate that design properties, such as obliviousness and quantification, can improve the modularity of software systems, thereby reducing the effort of composing design models. However, there is no empirical knowledge about how these design properties impact model composition effort. This paper, therefore, performs an empirical study to understand this impact. The main contributions are: (i) quantitative indicators to evaluate to what extent such design properties impact model composition effort; (ii) an objective evaluation of the impact of such modularity properties in 26 versions of two software projects by using statistical tests; and (iii) lessons learned on whether (and how) modularity anomalies related to misuse of quantification and obliviousness in the input models can significantly increase model composition effort.