Wow thanks for all the great advice and info.
Raging Bull wrote: ↑June 15th, 2020, 10:52 pm
take off a branch wherever there is more than one branch is coming off the trunk in the same place.
That gave me a concrete place to start without having to worry too much yet about the best trunk line.
I had read that bottle brushes can take a hard pruning especially after having flowered.
I took off some of the branches where several come out at the same spot as suggested, and when I started there were a few more that seemed natural to take off (crossing through the tree, on the inside of a curve, etc.), and I'm going to take of anything long that looks like I could use it to plant as a cutting

.
It's looking a little cleaner now.
There are still a couple of spots where branches seem to be twisting around each other that look a bit tricky to cut. Also I'm not sure yet which to keep or whether it could work keeping both. So for now just leaving them and when it's pruned down more maybe I'll get a better idea (and better photos

)
shibui wrote: ↑June 16th, 2020, 8:13 am
does not have a variety name
Regarding the name, it was a Callistemon Laevis, but when searching google seems to send me to M. Citrina, some sites say it's a variety that flowers four times a year, other searches gave rugulosis. I saw on here that Starfox had asked the question about the same 'Laevis' that he found in a nursery.
shibui wrote: ↑June 16th, 2020, 8:13 am
'sort out the roots early'.
Regarding the roots:
I scratched around the surface a bit with a chopstick, trying to move some of the dirt down around the trunk. There are a couple of surface roots, one big one that's clearly not 'radial' in the sense of good nebari, another one that might be ok, and a bunch of smaller roots on the surface.
I noticed this kind of felt or fabric around the base that looks like perhaps some medium that it was started in before potting in soil. Is there such a thing?
Another thing is that there are lots of little roots poking out the bottom holes of the pot. I didn't notice at first because it actually was sold in two pots, one slipped inside the other. I haven't yet taken it out to have a better look at the roots, but so far I get the impression that if it's not already root bound, it will be pretty soon.
shibui wrote: ↑June 16th, 2020, 8:13 am
Now would be an ideal time for you to check the roots and do some work if necessary. Repot and root work can be combined with your proposed first hard pruning without any danger to the tree.
Are you suggesting that I bare-root it (or almost) once it's been pruned down more?
Or just brush away as much of the top dirt as possible to see where the trunk goes to, or where some nice radial roots start?
I imagine in both cases I should then cut off quite a lot of the bottom roots?
And in either case should I then plant it back in the pot that it's already in to let it keep growing a while or start going for something smaller?
Ps. Just feel like I need to mention, I'm doing this without any proper tools; just some secateurs and scissors, kitchen fork, chopstick
