Indented tube flows are discussed when the characteristic Reynolds number K is large, the oncoming flow is fully developed and the indentations are slowly varying. The range of the theory in an allied paper (1) is extended to steady or unsteady asymmetric channel flows with α = O(K–1), and to symmetric tube flows with α = O(K–1), where α is a typical slope of the constriction. In the first regime here an upstream interaction takes place over a large length scale, forced by the transverse pressure gradient acting in the channel core, although oscillations of sufficiently high frequency in the wall shape can suppress this upstream response. The long-scale interaction is believed to occur ahead of any severe asymmetric distortion in steady channel flow, however. The second regime involves an elliptic core flow as the indentation length is shortened, but the wall layer is effectively unaltered ahead of the indentation.