Hundreds of copy number variants are complex and multi-allelic, in that they have many structural alleles and have rearranged multiple times in the ancestors who contributed chromosomes to current humans. Not only are the relationships of these multi-allelic CNVs (mCNVs) to phenotypes generally unknown, but many mCNVs have not yet been described at the basic levels-alleles, allele frequencies, structural features-that support genetic investigation. To date, most reported disease associations to these variants have been ascertained through candidate gene studies. However, only a few associations have reached the level of acceptance defined by durable replications in many cohorts. This likely stems from longstanding challenges in making precise molecular measurements of the alleles individuals have at these loci. However, approaches for mCNV analysis are improving quickly, and some of the unique characteristics of mCNVs may assist future association studies. Their various structural alleles are likely to have different magnitudes of effect, creating a natural allelic series of growing phenotypic impact and giving investigators a set of natural predictions and testable hypotheses about the extent to which each allele of an mCNV predisposes to a phenotype. Also, mCNVs' low-to-modest correlation to individual single-nucleotide polymorphisms (SNPs) may make it easier to distinguish between mCNVs and nearby SNPs as the drivers of an association signal, and perhaps, make it possible to preliminarily screen candidate loci, or the entire genome, for the many mCNV-disease relationships that remain to be discovered.