Multi-generational studies of organisms in the wild give a unique opportunity to investigate the genetic basis of traits, and of fitness itself. For species of conservation concern, knowledge of the genetic architecture of traits linked to fitness will enable more accurate predictions of adaptive potential, and can also improve our general understanding of the forces maintaining genetic variation despite the effects of drift and inbreeding. Hihi (stitchbird, Notiomystis cincta) are a threatened endemic New Zealand passerine that have been undergoing intensive conservation management since the 1980s. They have been studied extensively over that time and are a model species for successful ongoing reintroduction biology. Pedigree, reproductive and morphological data is available for the Tiritiri Matangi island sanctuary population dating back to 2005, and we have recently designed a 55K SNP chip for hihi and genotyped 1,475 individuals. We used this data to determine the genomic architecture of three morphological traits, all of which are linked to fitness, using genome wide association scans (GWAS). We demonstrate that all traits are influenced by many loci distributed throughout the genome, suggesting that future adaptation in this threatened species may be constrained by interactions with other linked traits.