The occurrence of topologically random channel networks in the presence of strong environmental controls does not necessarily indicate that network topology is insensitive to such controls. In areas where environmental controls have a preferred orientation, certain topologically distinct channel networks may be promoted where networks of a given magnitude flow in one direction and inhibited where they flow in another; but these biases in network topology may compensate for one another so effectively that they do not give rise to identifiable systematic deviations from topological randomness. This theme is illustrated by analyses of magnitude-4 channel networks from three areas in southeastern Australia. Goodness-of-fit tests indicate that the exhaustive samples of networks from these areas could have been drawn from topologically random populations. However, similar tests applied to subsamples selected according to network flow direction reveal biases in network topology in two of the areas. These biases, which are apparently due to microclimatic controls, signify that, although the networks in each area may belong to a topologically random population, they are not composed of randomly merging stream channels.