Traditional management practices are usually thought to be sustainable. The Maya manage Sabal (Arecaceae) palms in homegardens, using their leaves for thatching. The sustainability of such production systems depends on the long-term persistence of palm populations, whereas resource availability also depends on the number of leaves on individual palms. We examined how leaf harvest affects Sabal yapa and S. mexicana population growth rates (λ) and leaf production, comparing traditional and alternative harvest regimes in terms of sustainability and productivity. Demographic, harvest and leaf production data were recorded for three years in two homegardens. We used general integral projection models linked to leaf-production models to describe population dynamics and productivity. Harvest had no effect on S. yapa's vital rates or on λ, but it changed the growth rate of individuals of S. mexicana, with a negligible impact on λ. Homegardens affected λ values, reflecting the species' ecological affinities. S. mexicana, introduced from mesic forests, required watering and shade; therefore, its population declined rapidly in the homegarden that lacked both water and shade. The λ of the xerophilic S. yapa was slightly larger without watering than with watering. Palms usually compensated for leaf extraction, causing the number of leaves harvested per individual to increase with harvest intensity. Nevertheless, traditional management is relatively mild, allowing standing leaves to accumulate but reducing the homegarden's yield. Apparently, the Maya do not seek to maximize annual production but to ensure the availability of large numbers of leaves in homegardens. These leaves may then be used when the entire roof of a hut needs to be replaced every few years.