Crop diversification has been introduced as an environmental strategy in the ‘Greening’ of the EU Common Agricultural Policy (CAP) for 2015–2020. The primary target of crop diversification is soil and ecosystem resilience, but claims for potential benefits for farmland biodiversity are also common. However, understanding of relationships between the number (compositional heterogeneity) and spatial arrangement (configurational heterogeneity) of crop fields and biodiversity is generally poor, making such claims relatively unfounded. In this study, we monitored crop and farmland bird diversity on 178 farms across Sweden's main agricultural areas. From a pre-implementation assessment, we show that >97% of the assessed farms would not be required to change their management under the CAP crop diversification measure (minimum of three crops for farms with 30+ ha), suggesting that this measure has generated little change on Swedish farms. While accounting for non-crop elements and farming system (conventional or organic), we show that crop structural diversity (i.e. the management and vegetation structure of crops) rather than crop diversity senso lato positively affected richness of non-crop breeding bird species with stronger effects in arable, compared with forest-dominated landscapes. No such effects were observed among field-nesting farmland bird species. Organic farming had little influence on farmland birds with positive effects only in the most arable-dominated landscapes and for field-nesting species only. In forest-dominated landscapes, organic farms even held lower field-nester densities compared with conventional farms, possibly due to the dominance of grasslands on organic farms that in these landscapes support lower densities of field-nesting species compared with cereals. Policy implications. Our study illustrates the importance of a consideration of structural instead of species diversity of crops for biodiversity, in this case farmland birds. We also underline the absence of such a distinction in current EU Common Agricultural Policy Greening, while simultaneously setting levels on crop diversification too low resulting in little to no change in landscape-scale crop diversity on Swedish farmland. We recommend that future efforts to manage farmland biodiversity should include ways of increasing the structural diversity of crops at the scale of farms and landscapes.