To predict if a threatened species can adapt to changing selective pressures, it is crucial to understand the genetic basis of adaptive traits, especially in species historically affected by severe bottlenecks. We estimated the heritability of three hihi (Notiomystis cincta) morphological traits known to be under selection (nestling tarsus length, body mass and head–bill length) using 523 individuals and 39 699 single nucleotide polymorphisms (SNPs) from a 50 K Affymetrix SNP chip. We then examined the genetic architecture of the traits via chromosome partitioning analyses and genome-wide association scans (GWAS). Heritabilities estimated using pedigree relatedness or genomic relatedness were low. For tarsus length, the proportion of genetic variance explained by each chromosome was positively correlated with its size, and more than one chromosome explained significant variation for body mass and head–bill length. Finally, GWAS analyses suggested many loci of small effect contributing to trait variation for all three traits, although one locus (an SNP within an intron of the transcription factor HEY2) was tentatively associated with tarsus length. Our findings suggest a polygenic nature for the morphological traits, with many small effect size loci contributing to the majority of the variation, similar to results from many other wild populations. However, the small effective population size, polygenic architecture and already low heritabilities suggest that both the total response and rate of response to selection are likely to be limited in hihi.