Short insertions, deletions (INDELs) and larger structural variants have been increasingly employed in genetic association studies, but few improvements over SNP-based association have been reported. In order to understand why this might be the case, we analysed two publicly available datasets and observed that 63% of INDELs called in A. thaliana and 64% in D. melanogaster populations are misrepresented as multiple alleles with different functional annotations, i.e. where the same underlying variant is represented by inconsistent alignments leading to different variant calls. To address this issue, we have developed the software Irisas to reclassify and re-annotate these variants, which we then used for single-locus tests of association. We also integrated them to predict the functional impact of SNPs, INDELs, and structural variants for burden testing. Using both approaches, we re-analysed the genetic architecture of complex traits in A. thaliana and D. melanogaster. Heritability analysis using SNPs alone explained on average 27% and 19% of phenotypic variance for A. thaliana and D. melanogaster respectively. Our method explained an additional 11% and 3%, respectively. We also identified novel trait loci that previous SNP-based association studies failed to map, and which contain established candidate genes. Our study shows the value of the association test with INDELs and integrating multiple types of variants in association studies in plants and animals.