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You can produce your own briquettes and logs from your garden waste. Rake up leaves and store in a pile. Collect grass clippings in a pile also.
If you wish to burn as much of your garden waste as possible, you can mix wood pieces or chips with the leaves and grass. Take all your small stems and twigs from your pruning and garden waste, and chop them into short pieces that are a half inch to one inch long maximum. This is very similar to the way you would chop fire wood. You can use a hatchet and chopping block to do this, or a machete and chopping block; alternatively they can be processed through a wood chipper. If using a wood chipper, larger branches and stems can be used and reduced to wood chips.
If possible, collect lots of old newspaper. Newspaper is made from wood pulp, and burns well.