We study branching-time temporal description logics (BTDLs) based on the temporal logic CTL in the presence of rigid (time-invariant) roles and general TBoxes. There is evidence that, if full CTL is combined with the classical ALC in this way, reasoning becomes undecidable. In this paper, we begin by substantiating this claim, establishing undecidability for a fragment of this combination. In view of this negative result, we then investigate BTDLs that emerge from combining fragments of CTL with lightweight DLs from the EL and DL-Lite families. We show that even rather inexpressive BTDLs based on EL exhibit very high complexity. Most notably, we identify two convex fragments which are undecidable and hard for non-elementary time, respectively. For BTDLs based on DL-Litebool, we obtain tight complexity bounds that range from PSPACE to EXPTIME.