We present an efficient technique to study the 1D evolution of instability-generated structure in winds of hot stars out to very large distances (~1000 stellar radii). This technique makes use of our previous finding that external forces play little rôle in the outer evolution of structure. Rather than evolving the entire wind, as is traditionally done, the technique focuses on a representative portion of the structure and follows it as it moves out with the flow. This requires the problem to be formulated in a moving reference frame. The lack of Galilean invariance of the spherical equations of hydrodynamics is circumvented by recasting them in a pseudo-planar form. By applying the technique to a number of problems we show that it is fast and accurate, and has considerable conceptual advantages. It is particularly useful to test the dependence of solutions on the Galilean frame in which they were obtained. As an illustration, we show that, in a one-dimensional approximation, the wind can remain structured out to distances of more than 1300 stellar radii from the central star.