Reconstructing phylogenies from intraspecific data (such as human mitochondrial DNA variation) is often a challenging task because of large sample sizes and small genetic distances between individuals. The resulting multitude of plausible trees is best expressed by a network which displays alternative potential evolutionary paths in the form of cycles. We present a method ("median joining" [MJ]) for constructing networks from recombination-free population data that combines features of Kruskal's algorithm for finding minimum spanning trees by favoring short connections, and Farris's maximum-parsimony (MP) heuristic algorithm, which sequentially adds new vertices called "median vectors", except that our MJ method does not resolve ties. The MJ method is hence closely related to the earlier approach of Foulds, Hendy, and Penny for estimating MP trees but can be adjusted to the level of homoplasy by setting a parameter epsilon. Unlike our earlier reduced median (RM) network method, MJ is applicable to multistate characters (e.g., amino acid sequences). An additional feature is the speed of the implemented algorithm: a sample of 800 worldwide mtDNA hypervariable segment I sequences requires less than 3 h on a Pentium 120 PC. The MJ method is demonstrated on a Tibetan mitochondrial DNA RFLP data set.