Brazil recently began granting timber concessions in public forests to promote sustainable forest use. The effectiveness of this strategy hinges on the design and implementation of the concessions themselves as well as their competitive position within the logging sector as a whole. There is, however, a lack of information on the competitive interaction between legal and illegal logging and its effects on concessions profits. We address this knowledge gap by using a spatially explicit simulation model of the Amazon timber industry to examine the potential impact of illegal logging on timber concessions allocation and profits in a 30-year harvest cycle. In a scenario in which illegal logging takes place outside concessions, including private and public "undesignated" lands, concession harvested area would decrease by 59% due to competition with illegal logging. Moreover, 29 out of 39 National Forests (≈74%) would experience a decrease in harvested area. This "leakage" effect could reduce concession net rents by up to USD 1.3 Billion after 30 years. Federal and State "undesignated" lands, if not adequately protected, could have 40% of their total volume illegally harvested in 30 years. Our results reinforce the need to invest in tackling illegal logging, if the government wants the forest concessions program to be successful.