The idea of ‘flushes’ confuses me a bit. Does being ‘single flush’ mean that for an entire season, the plant will only grow once? Or for a period of time?
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**Disclaimer - this is just my experience. Some here have different luck with getting these to grow a second flush of branches/leaves from pruning.
For burning bushes, when you cut the growing tip off of a branch it usually stops growing for the year. It will set buds for next year, but no more growth/extension on the branches that have been pruned. Next year it will grow out like normal. They are super predictable with this and you can build ramification, it's just slower. I'll post some photos of mine this evening if that's helpful that shows exactly what I'm talking about.
Maples, elms, etc are the opposite, you can often prune in the summer and they will respond with all kinds of good stuff (backbudding into old wood, growth to build ramification, tighter internodes, etc.) - they make new branches in response to pruning.