The paper investigates the task of inferring a phylogenetic tree of languages from the collection of word lists made available by the Automated Similarity Judgment Project. This task involves three steps: (1) computing pairwise word distances, (2) aggregating word distances to a distance measure between languages and inferring a phylogenetic tree from these distances, and (3) evaluating the result by comparing it to expert classifications. For the first task, weighted alignment will be used, and a method to determine weights empirically will be presented. For the second task, a novel method will be developed that attempts to minimize the bias resulting from missing data. For the third task, several methods from the literature will be applied to a large collection of language samples to enable statistical testing. It will be shown that the language distance measure proposed here leads to substantially more accurate phylogenies than a method relying on unweighted Levenshtein distances between words.