A critical, but largely unexamined assumption in the debate over reform policy design, concerns the complementarity or substitutability of market competition and private ownership in increasing firm efficiency. We analyse a simple Cournot model that distinguishes two aspects of privatization interacting with market opening: privatization of a firm and privatization of its competitors. Under plausible conditions, the model implies that privatizing a firm is a substitute for exposing it to competitive markets, but privatizing its competitors is complementary. Our empirical analysis uses augmented 3-factor translog production functions estimated on 1992-99 panel data for 13,288 Russian manufacturing enterprises. We find that nonstate ownership of a firm reduces the marginal efficiency impact from product market dispersion, but the share of its competitors that are nonstate increases this marginal impact. Disaggregating nonstate ownership, we find that the shares of competitors in all three nonstate types are complementary with dispersed market structure, where the strongest complementarity involves foreign ownership. The evidence suggests that an important indirect impact of private ownership may be the intensification of market competition, and thus that competition only among state-owned enterprises may be ineffectual in stimulating them to increase efficiency.