I am thinking a small sucking insect, thrips or so. Have you checked for tiny bugs?
Hmm... You may be right... I've found three small bugs under the leaves. Don't know what kind. See the picture below (the bug is a little squashed). The body is about 3 mm long.
Two things surprise me me though:
* It is hard to believe that 3-5 bugs could cause that much damage.
* These bugs are winged so they could easily fly from one branch to another. On my tree, the damage is quite focused - one branch is damaged, and another branch has no problems.
Anyway, I'll watch the tree carefully and will make sure to remove all bugs I find.
Thank you for your suggestion.