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This paper studies the case where an outside patent holder licenses its vertical product innovation to two Cournot competitors. It is found that, under a fixed-fee contract, the patent holder prefers exclusive licensing. However, under a royalty or two-part tariff contract, the patent holder favours non-exclusive licensing. Moreover, in contrast to the standard argument by Kamien and Tauman, we show that, from the perspective of the patentee, royalty licensing can be superior to fixed-fee licensing, if the degree of innovation is small. Two-part tariff licensing generates a monopoly outcome in the final market and hence reduces both consumer surplus and social welfare, if the innovation is low.