In evolutionary multiobjective optimization, the task of the optimizer is to obtain an accurate and useful approximation of the true Pareto-optimal front. Proximity to the front and diversity of solutions within the approximation set are important requirements. Most established multiobjective evolutionary algorithms (MOEAs) have mechanisms that address these requirements. However, in many-objective optimization, where the number of objectives is greater than 2 or 3, it has been found that these two requirements can conflict with one another, introducing problems such as dominance resistance and speciation. In this paper, two diversity management mechanisms are introduced to investigate their impact on overall solution convergence. They are introduced separately, and in combination, and tested on a set of test functions with an increasing number of objectives (6-20). It is found that the inclusion of one of the mechanisms improves the performance of a well-established MOEA in many-objective optimization problems, in terms of both convergence and diversity. The relevance of this for many-objective MOEAs is discussed.