Recently, Hierarchical Clustering (HC) has been considered through the lens\nof optimization. In particular, two maximization objectives have been defined.\nMoseley and Wang defined the \\emph{Revenue} objective to handle similarity\ninformation given by a weighted graph on the data points (w.l.o.g., $[0,1]$\nweights), while Cohen-Addad et al. defined the \\emph{Dissimilarity} objective\nto handle dissimilarity information. In this paper, we prove structural lemmas\nfor both objectives allowing us to convert any HC tree to a tree with constant\nnumber of internal nodes while incurring an arbitrarily small loss in each\nobjective. Although the best-known approximations are 0.585 and 0.667\nrespectively, using our lemmas we obtain approximations arbitrarily close to 1,\nif not all weights are small (i.e., there exist constants $\\epsilon, \\delta$\nsuch that the fraction of weights smaller than $\\delta$, is at most $1 -\n\\epsilon$); such instances encompass many metric-based similarity instances,\nthereby improving upon prior work. Finally, we introduce Hierarchical\nCorrelation Clustering (HCC) to handle instances that contain similarity and\ndissimilarity information simultaneously. For HCC, we provide an approximation\nof 0.4767 and for complementary similarity/dissimilarity weights (analogous to\n$+/-$ correlation clustering), we again present nearly-optimal approximations.\n