Eucalyptus can be cut back hard . I personally wouldn't cut back like a hair cut short back and sides , it will ruin the natural shape and eventually you will have a far more dense tree in the future. I'd crown thin it removing branches inside the tree to let light pass through and it will show off the fantastic bark and structure of the tree . I've seen E. niphophlia ( white bark one ) where its been crown lifted right up so it just the top canopy it looks quite good and it cast hardly any shade .
I'd follow Perki's advice above and we will be in the best time to prune eucalyptus soon which is febuary/March, just before they begin to grow actively again. I have one which I've pallarded for the last few years and it always grows back thick and lush but I want to coppice it this year and retrain as a smaller multistem because I don't want to have to go up a ladder every year now to cut out the congested branches. Luckily they are a very easy tree to keep an open framework on and they don't cast that much shade if you do it properly (or at least you can control the amount of shade they give). I regularly hack bits off, any time of year, when they get in the way but controlled pruning is best done soon.
Many thanks Perki and thevicorian. I will indeed follow your advice and thin it out and reduce the height in Feb/March because like you I don't want to have to climb up the ladder to prune it in the future. Great, everyone is always so helpful on this site
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I want to give it a huge haircut as it's taking up half the garden- will it survive a server prune do you know ?
I have one which I've pallarded for the last few years and it always grows back thick and lush but I want to coppice it this year and retrain as a smaller multistem because I don't want to have to go up a ladder every year now to cut out the congested branches. Luckily they are a very easy tree to keep an open framework on and they don't cast that much shade if you do it properly (or at least you can control the amount of shade they give). I regularly hack bits off, any time of year, when they get in the way but controlled pruning is best done soon.