Distance-based phylogenetic reconstruction methods use the evolutionary distances between species in order to reconstruct the tree spanning them. The evolutionary distance between two species, which is computed from their DNA (or protein) sequences, is typically considered as a fixed function of these sequences, predetermined by the assumed model of evolution. This article continues the line of research that attempts to adjust to each given set of input sequences a distance function which maximizes the expected accuracy of the reconstructed tree. Specifically, we present methods for selecting distance functions that considerably improve the accuracy of quartets constructed by the four-point method in Kimura's 2-parameter model, where special emphasis is given to the case of non-homogenous quartets.