The expansion of agriculture into tropical forest frontiers is one of the primary drivers of the global extinction crisis, resulting in calls to intensify tropical agriculture to reduce demand for more forest land and thus spare land for nature. Intensification is likely to reduce habitat complexity, with profound consequences for biodiversity within agricultural landscapes. Understanding which features of habitat complexity are essential for maintaining biodiversity and associated ecosystem services within agricultural landscapes without compromising productivity is therefore key to limiting the environmental damage associated with producing food intensively. Here, we focus on oil palm, a rapidly expanding crop in the tropics and subject to frequent calls for increased intensification. One promoted strategy is to remove epiphytes that cover the trunks of oil palms, and we ask whether this treatment affects either biodiversity or yield. We experimentally tested this by removing epiphytes from four-hectare plots and seeing if the biodiversity and production of fruit bunches 2 months and 16 months later differed from equivalent control plots where epiphytes were left uncut. We found a species-rich and taxonomically diverse epiphyte community of 58 species from 31 families. Epiphyte removal did not affect the production of fresh fruit bunches, or the species richness and community composition of birds and ants, although the impact on other components of biodiversity remains unknown. We conclude that as they do not adversely affect palm oil production, the diverse epiphyte flora should be left uncut. Our results underscore the importance of experimentally determining the effects of habitat complexity on yield before introducing intensive methods with no discernible benefits.