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From The Ramshead, head north following the line of knolls over the top of The Corrie and Couloiir runs.
This is fairly undulating terrain but stay north for around 500 metres, following this, the terrain to left will roll down far more mellowly towards Leatherbarrel Creek.
Observe to the left again and you will see the boundary of the catchment as the river turns towards you and will most likely disappear under snow below the knolls you are on.
The catchment boundary is significant, and once you pass it you will most likely be able to see Cootapatamba Hut and the Swamp Plain River.
Drop down towards whenever you like, and you will most likely be able to ski right down to the hut, on the very mellow terrain.
For the inverse journey, simply skin up to the ridgeline to the east of Cootapatamba hut, and follow it south to The Ramshead.
This will only take an hour or so down, and around two hours up.