The challenge faced by governments in the regulation of powerful private actors has allegedly intensified in recent years. This study explores the means at the disposal of governments, and their effectiveness, with respect to the regulation of private actors that demonstrate considerable independence and political efficacy. It is argued that a modified ‘Contextual Interaction Theory’ (CIT), which focuses on the interaction between generic policy instruments (carrots, sticks, and sermons) and target group attributes (motivation, information, and power), and is augmented by a consideration of a separate institutional dimension, offers a useful analytical framework for understanding both the challenge faced by governments and the options for dealing with it. This framework is applied to a study of the introduction of ‘new accountability’ to Australian and Israeli non-government schools. The use of the standard CIT lenses helps explain Australian success and Israeli government failure in the introduction of new accountability. Australian success is attributable to a judicious mix of ‘hard’ and ‘soft’ instruments that favorably impacted target group information and motivation. In Israel, in contrast, policy instrument mixes failed to alter the main target group's oppositional stance. Institutional engineering, however, could provide a promising way for Israeli policymakers to enhance policy instrument effectiveness, by influencing target group power and motivation.