In this paper, we evaluate the relative performance of competing approaches for estimating phylogenies from incomplete distance matrices. The direct approach proceeds with phylogenetic reconstruction while ignoring missing cells, whereas the indirect approach proceeds by estimating the missing distances prior to phylogenetic analysis. Two distinct indirect procedures based on the ultrametric inequality and the four-point condition are further compared. Using simulations, we show that more reliable results are obtained when such indirect methods are used. Expectedly, the phylogenies become less accurate as the percentage of missing cells increases, but combining different estimation methods greatly improves the accuracy. An application to bat phylogeny confirms the results obtained in the simulation study and illustrates the effect of missing distances in the construction of supertrees.