The expansion of agricultural land remains one of the main drivers of deforestation in tropical regions. Stronger land property rights could possibly enable farmers to increase input intensity and productivity on the already cultivated land, thus reducing incentives to expand their farms by deforesting additional land. This hypothesis is tested with data from a panel survey of farm households in Sumatra. The survey data are combined with satellite imageries to account for spatial patterns, such as historical forest locations. Results show that plots for which farmers hold formal land titles are cultivated more intensively and are more productive than untitled plots. However, due to land policy restrictions, farmers located at the historic forest margins often do not hold formal titles. Without land titles, these farmers are less able to intensify and more likely to expand into the surrounding forest land to increase agricultural output. Indeed, forest closeness and past deforestation activities by households are found to be positively associated with current farm size. In addition to improving farmer's access to land titles for non-forest land, better recognition of customary land rights and more effective protection of forest land without recognized claims could be useful policy responses. •Land titles raise farming intensity and productivity in Sumatra, Indonesia.•Thus, farmers with land titles have lower deforestation incentives to increase production.•Farmers at the forest margins are unlikely to hold land titles, hence less able to intensify.•Farmers at the forest margins have larger farms, are more involved in deforestation.•More land titling could incentivize forest-sparing agricultural intensification.