We describe an efficient method of calculating the radiation pressure resul
ting from spectral lines, including all the terms in the velocity gradient
tensor. We apply this method to calculate the two-dimensional, time-depende
nt structure of winds from luminous discs. Qualitative features of our new
models are very similar to those we calculated including only the dominant
terms in the tensor. In particular, we find that models which displayed uns
teady behaviour in our earlier paper are also unsteady with the new method,
and gross properties of the winds, such as mass-loss rate and characterist
ic velocity, are not changed by the more accurate approach. The largest cha
nge caused by the new method is in the disc-wind opening angle: winds drive
n only by the disc radiation are more polar with the new method, whilst win
ds driven by the disc and central object radiation are typically more equat
orial. In the closing discussion, we provide further insight into the way t
he geometry of the radiation field and consequent flow determine the time p
roperties of the flow.