This paper aims to understand the practical features of hierarchies of morphological segmentations, namely the quasi-flat zones hierarchy and watershed hierarchies, and to evaluate their potential in the context of natural image analysis. We propose a novel evaluation framework for the hierarchies of partitions designed to capture various aspects of those representations: precision of their regions and contours, possibility to extract high quality horizontal cuts and optimal non-horizontal cuts for image segmentation, and the ease of finding a set of regions representing a semantic object. This framework is used to assess and to optimize hierarchies with respect to the possible pre- and post-processing steps. We show that, used in conjunction with a state-of-the-art contour detector, watershed hierarchies are competitive with the complex state-of-the-art methods for hierarchy construction. In particular, the proposed framework allows us to identify a watershed hierarchy based on a novel extinction value, the number of parent nodes that outperforms the other hierarchies of morphological segmentations. This coupled with the fact that watershed hierarchies satisfy clear global optimality properties and can be efficiently computed on large data, make them valuable candidates for various computer vision tasks.