I have often taken the tip of some Echeveria species in order to promote branching. The branches are then used as cuttings. My process involves first taking away the tip, leaving all the leaves below the cut attached to the rosette's main trunk. A "naked" stem does not always generate new pups and may die as a result. Keeping the leaves will ensure new offsets start to poke out of the leaf-bases. As the pups grow, I take more leaves out of the main trunk and I often root the leaves as well. The end result is a "mound" of rosettes from which I can take new rosette cuttings.
I never do this process to the compact Echeverias. Unfortunately, all my plants are available at nurseries that do not keep (or do not get the plants with) the species lables. I identified one of my "compact" Echeverias as E. Lilacina, which is too compact to treat this way, because the main trunk is too short. On the other hand, I may take-off the tip if it has rotted (for whatever reason) or was damaged. In that case, would the offsetting rosettes be too squeezed and distorted? Would I be able to take good-looking pups this way, or should I resort to leaf-cuttings?