Comparative genomic hybridization (CGH) is a laboratory method to measure gains and losses in the copy number of chromosomal regions in tumor cells. It is hypothesized that certain DNA gains and losses are related to cancer progression and that the patterns of these changes are relevant to the clinical consequences of the cancer. It is therefore of interest to develop models which predict the occurrence of these events, as well as techniques for learning such models from CGH data. We continue our study of the mathematical foundations for inferring a model of tumor progression from a CGH data set that we started in Desper et al. (1999). In that paper, we proposed a class of probabilistic tree models and showed that an algorithm based on maximum-weight branching in a graph correctly infers the topology of the tree, under plausible assumptions. In this paper, we extend that work in the direction of the so-called distance-based trees, in which events are leaves of the tree, in the style of models common in phylogenetics. Then we show how to reconstruct the distance-based trees using tree-fitting algorithms developed by researchers in phylogenetics. The main advantages of the distance-based models are that 1) they represent information about co-occurrences of all pairs of events, instead of just some pairs, 2) they allow quantitative predictions about which events occur early in tumor progression, and 3) they bring into play the extensive methodology and software developed in the context of phylogenetics. We illustrate the distance-based tree method and how it complements the branching tree method, with a CGH data set for renal cancer.