We introduce a new notion of non-manipulability by groups, based on the idea that some of the agreements among a set of potential manipulators may be credible, while others may not. The derived notion of immunity to credible manipulations by groups is intermediate between individual and group strategy-proofness. We show that our new concept has bite, by applying it to the analysis of a large family of public good decision problems in separable environments, where there exist many attractive strategy-proof rules that are, however, manipulable by groups. In these environments we show that some of these rules are indeed, immune to credible group manipulations, while others are not. We provide characterization results that separate these two classes.