Earlier analyses of valley networks on Mars often concluded that they were poorly integrated, immature drainage systems. Consequently, surface runoff from precipitation was generally thought to be an unimportant geomorphic process. Combination of Mars Global Surveyor (MGS) imaging and altimetry data sets, however, provides a vast improvement in image clarity and resolution. Although we have used the same defining characteristics for valley networks as used in previous work, our mapping in the Martian highlands reveals up to an order of magnitude higher values for the number of valleys, total valley length, and drainage density. Segments can now be mapped a greater distance with the result that the heads of numerous systems reach right up to the drainage divides. Moreover, MGS data show that many previously mapped, unconnected, low-stream-order segments are part of larger, integrated, mature drainage networks. In light of these new data, it is likely that surface runoff (and, by inference, precipitation) played an important role in the sculpting of large regions of the Martian landscape early in the planet's history.