Science studies has shown us why science and 'technology cannot always solve technical problems in the public domain. In particular, the speed of political decision-making is faster than the speed of scientific consensus formation. A predominant motif over recent years has been the need to extend the domain of technical decision-making beyond the technically qualified élite, so as to enhance political legitimacy. We argue, however, that the 'Problem of Legitimacy' has been replaced by the 'Problem of Extension' - that is, by a tendency to dissolve the boundary between experts and the public so that there are no longer any grounds for limiting the indefinite extension of technical decision-making rights. We argue that a Third Wave of Science Studies - Studies of Expertise and Experience (SEE) - is needed to solve the Problem of Extension. SEE will include a normative theory of expertise, and will disentangle expertise from political rights in technical decision-making, The theory builds categories of expertise, starting with the key distinction between interactive expertise and contributory expertise. A new categorization of types of science is also needed. We illustrate the potential of the approach by reexamining existing case studies, including Brian Wynne's study of Cumbrian sheep farmers. Sometimes the new theory argues for more public involvement, sometimes for less. An Appendix describes existing contributions to the problem of technical decision-making in the public domain.