One of the best investments I made around 25 years ago was an electric shredder. All branches below about 1" diameter and all woody stuff and leaves get shredded to make mulch. Bigger branches are cut up and go into the wood bin for the fire.. Kitchen waste is composted, grass clippings are left to be re-absorbed into the ground. No green waste ever goes down the tip.
I shred broad bean stalks, they compost down much faster then.
The hardest plant to dispose of is the New Zealand flax
https://en.wikipedia.org/wiki/Flax_in_New_Zealand. The fibres are too strong to be shredded or mown. So if a flax plant needs to be removed, they usually get dumped in the bush at the top of the garden for a few years until it has decomposed.
Everything here grows at twice the rate of in the UK, blink an eye and the bush has advanced down the garden.
No Kiwi should be without a chainsaw