That's pretty much what I had in mind to try. Aerate, gypsum and then
fertilise.
I'm not planning on starting the whole thing till after the summer and
assuming the water situation improves. We're watering too infrequently
enough now anyway to make it worthwhile I feel. The gypsum would probably
just blow of the surface like dust! Maybe by next spring we can have a green
lawn or if there's no water I may as well rip it up and start from scratch!?
Thanks for the advice!


You could try the gypsum on the existing area, aerate it, and fertilise
well. Oh, aerate first, then gypsum, then fertilise.

Top dressing before you fertilise wouldn't be a bad idea either

It should fix the problem.

Is the areas of compaction due to people walking on it? If so, then
consider
a path in that area. Trying to get grass to go on a regular walk track is
generally a lost cause

If the area you live in has a chance of getting water restrictions imposed
real soon, then I would consider leaving it for now.
Many lawns are brown here, as watering lawns is one of the first things to
be stopped.
We are at stage 4 here (think 4), and we are down to watering only by
buckets/watering cans, for 1hr in the morning and night. You can only
water
plants, no lawns, and no washing cars even with buckets amongst other
things.

Good luck