In [this paper][1], Kuznetsov mentions that the following triangulated categories have the Jordan-Holder properties

 - $\mathbf{D}(\Bbb P^1)$ and $\mathbf{D}(\Bbb P^1/\Gamma)$
 - connected Calabi-Yau categories
 - derived categories of curves of positive genus

These are the only examples of geometric triangulated categories with the Jordan-Holder property that I know of. Are there any others?


  [1]: http://arxiv.org/pdf/1304.0903v1.pdf