Empirical techniques commonly used in industrial organization to measure market power exertion typically assume imperfectly competitive behaviour by firms on only one side of the market. Firms on the other side are assumed to be perfectly competitive. In this paper we extend traditional NEIO methods by developing a method to estimate market power exertion when firms on both sides have potential market power. Using Monte Carlo simulations, we find that the model correctly estimates market power exercised by firms on either or both sides of a market and also correctly estimates firms' technology parameters. When applied to the US leaf tobacco market, findings indicate that cigarette manufacturers exert some monopsony power in purchasing leaf tobacco while producers, organized as a cartel, exhibit no countervailing monopoly market power.