When there is still the potential to cause damage or the ground needs protecting (patio or tidy lawn) we have found the following to be fairly effective
The double layer of logs helps to decrease the distance of fall and spread the force of impact, and the tyres are obviously there to take the brunt of the impact. You have to be accurate with discs and it works best when they land flat on the tyres. The tyres need replacing each time but it still works out much quicker than any other method I've tried.
Once you've got lower still you can condense the tyres at the base of the tree and start to take some bigger lumps. Keeping the other blocks in place helps to contain the lumps as they come down and deflect them into the base of the tree. You'd be amazed at how well this works and how much energy the tyres will absorb.
Certainly worked well on this Swamp cypress fell