The importance of trade and investment agreements for health is now widely acknowledged in the literature, with much attention now focused on the impact of investor-state dispute settlement (ISDS) mechanisms. However, much of the analysis of such agreements in the health field remains largely descriptive. We theorize the implications of ISDS mechanisms for health policy by integrating the concept of global constitutionalism with veto point theory. It is argued that attempts to constitutionalize investment law, through a proliferation of International Investment Agreements (IIAs), has created a series of new veto points at which corporations may seek to block new policies aimed at protecting or enhancing public health. The multiplicity of new veto points in this global "spaghetti bowl" of IIAs creates opportunities for corporations to venue shop; that is, to exploit the agreements, and associated veto points, through which they are most likely to succeed in blocking or deterring new regulation. These concepts are illustrated with reference to two case studies of investor-state disputes involving a transnational tobacco company, but the implications of the analysis are of equal relevance for a range of other industries and health issues.