Context The current Common Agricultural Policy (CAP) of the European Union includes three greening measures, which are partly intended to benefit farmland biodiversity. However, the relative biodiversity effects of the greening measures, including joint effects of landscape context, are not well understood. Objectives We studied the effects of increasing crop diversity, proportions of production grasslands and fallows, corresponding to CAP greening measures, on open farmland bird diversity, whilst controlling for the effects of distance to forests, field edge density and proportion of built-up areas. Methods We surveyed open farmland birds using territory mapping in Southern Finland. We modelled effects of greening measures and landscape structure on farmland birds (7642 territories) using generalised linear mixed models. Results Increasing proportions of grasslands increased farmland bird species richness and diversity in open farmland, whereas increasing proportions of fallows increased bird diversity. Increasing crop diversity benefited individual species, but not species richness or diversity. Increasing field edge densities consistently increased the species richness of all farmland species, in-field nesters and non-crop nesters, as well as total farmland bird diversity. The relative effect of edge density was much stronger compared to the three greening measures. Conclusions Our results show that promoting fallows and grasslands, in particular grazed grasslands and various types of semi-natural grasslands, has the highest potential to benefit farmland bird diversity. Maintaining or increasing field edge densities, currently not supported, seems to be of even more benefit. In open farmland, with little or no field edges, fallows and grasslands are particularly beneficial.