We show by means of several examples that robust statistical estimators present an excellent starting point for differentially private estimators. Our algorithms use a new paradigm for differentially private mechanisms, which we call Propose-Test-Release (PTR), and for which we give a formal definition and general composition theorems. Categories and Subject Descriptors H.2.0 [Information Systems]: Database Management-security, integrity and protection; G.3 [Mathematics of Computing]: Probability and Statistics--statistical computing General Terms Algorithms, Security and Theory