Additive genetic variance, V_A, is the key parameter for predicting adaptive and neutral phenotypic evolution. Changes in demography (e.g., increased close-relative inbreeding) can alter V_A, but how depends on the, typically unknown, gene action and allele frequencies across many loci. For example, V_A increases proportionally with the inbreeding coefficient when allelic effects are additive, but larger (or smaller) increases can occur when allele frequencies are unequal at causal loci with dominance effects. Here, we describe an experimental approach to assess the potential for rare, recessive alleles to inflate V_A under inbreeding. Applying a powerful paired pedigree design in Drosophila serrata, we measured 11 wing traits on half-sibling families bred via either random or sibling mating, differing only in homozygosity (not allele frequency). Despite close inbreeding and substantial power to detect small V_A, we detected no deviation from the expected additive effect of inbreeding on genetic (co)variances. Our results suggest the average dominance coefficient is very small relative to the additive effect, or that allele frequencies are relatively equal at loci affecting wing traits. We outline the further opportunities for this paired pedigree approach to reveal the characteristics of V_A, providing insight into historical selection and future evolutionary potential.