We propose to use optimally ordered orthogonal neighbor-joining (O $^{3}$ NJ) trees as a new way to visually explore cluster structures and outliers in multi-dimensional data. Neighbor-joining (NJ) trees are widely used in biology, and their visual representation is similar to that of dendrograms. The core difference to dendrograms, however, is that NJ trees correctly encode distances between data points, resulting in trees with varying edge lengths. We optimize NJ trees for their use in visual analysis in two ways. First, we propose to use a novel leaf sorting algorithm that helps users to better interpret adjacencies and proximities within such a tree. Second, we provide a new method to visually distill the cluster tree from an ordered NJ tree. Numerical evaluation and three case studies illustrate the benefits of this approach for exploring multi-dimensional data in areas such as biology or image analysis.