@RobertBaron has the same plan I use for long smokes or just for long cooks like lamb shoulders, I use new coals for those but almost always reuse my burnt coals again and again until they are not big enough.
I always put new coals in the BOTTOM of the chimney first and then the used on top of new. New coals always seem to light off faster and help to get the used going.
If the used coals are too small I don't get the air flow in the chimney good and it takes longer to start, if they all restart at all.
My Smokey Joe sees the coals from my 22" MT after a quick cook.. as soon as I'm done cooking I pull the grate off and take the charcoal baskets out using my Weber SS grabby tong and give them a shake and dump them in the SJ and close it up... few mins later they are OUT and cooled. This is WAY faster than closing all the vents on a 22" and waiting.
This is just what I do, it works for me..do what works best for you.
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