This paper deals with a general version of a two-stage model of R&D and product market competition. Our main goal is to characterize the structure of optimal R&D cartels where firms competing in a product market jointly decide R&D expenditure, as well as internal spillover, levels. We establish the firms would essentially always prefer extremal spillovers. Within the context of a standard specification, we provide conditions for the optimality of minimal spillover. As auxiliairy goal, a thorough generalization of previous results on the comparative performance of various R&D cooperation schemes is provided, dispensing with all objectionable assumptions.