Many layouts exist for visualizing phylogenetic trees, allowing to display the same information (evolutionary relationships) in different ways. For large phylogenies, the choice of the layout is a key element, because the printable area is limited, and because interactive on-screen visualizers can lead to unreadable phylogenetic relationships at high zoom levels. A visual inspection of available layouts for rooted trees reveals large empty areas that one may want to fill in order to use less drawing space and eventually gain readability. This can be achieved by using the nonlayered tidy tree layout algorithm that was proposed earlier but was never used in a phylogenetic context so far. Here, we present its implementation, and we demonstrate its advantages on simulated and biological data (the measles virus phylogeny). Our results call for the integration of this new layout in phylogenetic software. We implemented the nonlayered tidy tree layout in R language as a stand-alone function (available at https://github.com/damiendevienne/non-layered-tidy-trees), as an option in the tree plotting function of the R package ape, and in the recent tool for visualizing reconciled phylogenetic trees thirdkind (https://github.com/simonpenel/thirdkind/wiki).