Modified CRLB with Differential Privacy

It turns out that with differential privacy the Cramer-Rao lower bound (CRLB) is not achievable (too bad for MLE), but you can figure out what *is* achievable, and find estimators that do the trick. (See the interesting talk here by Feng Ruan, and the associated papers on his web site.) The key point is that estimation efficiency is degraded by privacy. The new frontier seems to me to be this: Let's go beyond stark "privacy" or "no privacy" situations, because in reality there is a spectrum of "epsilon-strengths" of "epsilon-differential" privacy.  (Right?)  Then there is a tension: I like privacy, but I also like estimation efficiency, and the two trade off against each other. So there is a choice to be made, and the optimum depends on preferences.