Dendrograms are graphical representations of binary tree structures resulting from agglomerative hierarchical clustering. In Life Science, a cluster heat map is a widely accepted visualization technique that utilizes the leaf order of a dendrogram to reorder the rows and columns of the data table. The derived linear order is more meaningful than a random order, because it groups similar items together. However, two consecutive items can be quite dissimilar despite proximity in the order. In addition, there are 2 n-1 possible orderings given n input elements as the orientation of clusters at each merge can be flipped without affecting the hierarchical structure. We present two modular leaf ordering methods to encode both the monotonic order in which clusters are merged and the nested cluster relationships more faithfully in the resulting dendrogram structure. We compare dendrogram and cluster heat map visualizations created using our heuristics to the default heuristic in R and seriation-based leaf ordering methods. We find that our methods lead to a dendrogram structure with global patterns that are easier to interpret, more legible given a limited display space, and more insightful for some cases. The implementation of methods is available as an R package, named ”dendsort”, from the CRAN package repository. Further examples, documentations, and the source code are available at [https://bitbucket.org/biovizleuven/dendsort/].