Influenza A virus contains regions of its segmented genome associated with ability to package the segments into virions, but many such regions are poorly characterised. We provide detailed predictions of the key locations within these packaging-associated regions, and their structures, by applying a recently-improved pipeline for delineating constrained regions in RNA viruses and applying structural prediction algorithms. We find and characterise other known constrained regions within influenza A genomes, including the region associated with the PA-X frameshift, regions associated with alternative splicing, and constraint around the initiation motif for a truncated PB1 protein, PB1-N92, associated with avian viruses. We further predict the presence of constrained regions that have not previously been described. The extra characterisation our work provides allows investigation of these key regions for drug target potential, and points towards determinants of packaging compatibility between segments.