Single k-reversible restarting automata are a special version of restarting automata which can be effectively learned from samples. We show that their power lies between GCSL and CSL. We show that their subclasses form an infinite hierarchy of classes of languages with respect to the reversibility level k and we also show that limiting types of allowed rewrites lowers the power of the model. Finally, we study their relation to strictly locally testable restarting automata.