A complicating factor in analyzing allopolyploid genomes is the possibility of physical interactions between homoeologous chromosomes during meiosis, resulting in either crossover (homoeologous exchanges) or non-crossover products (homoeologous gene conversion). Homoeologous gene conversion was first described in cotton by comparing SNP patterns in sequences from two diploid progenitors with those from the allopolyploid subgenomes. These analyses, however, did not explicitly consider other evolutionary scenarios that may give rise to similar SNP patterns as homoeologous gene conversion, creating uncertainties about the reality of the inferred gene conversion events. Here, we use an expanded phylogenetic sampling of high-quality genome assemblies from seven allopolyploid Gossypium species (all derived from the same polyploidy event), four diploid species (two closely related to each subgenome), and a diploid outgroup to derive a robust method for identifying potential genomic regions of gene conversion and homoeologous exchange. We found little evidence for homoeologous gene conversion in allopolyploid cottons, and that only two of the 40 best-supported events were shared by more than one species. We did, however, reveal a single, shared homoeologous exchange event at one end of chromosome 1, which occurred shortly after allopolyploidization but prior to divergence of the descendant species. Overall, our analyses demonstrated that homoeologous gene conversion and homoeologous exchanges are uncommon in Gossypium, affecting between zero and 24 genes per subgenome (0.0-0.065%) across the seven species. More generally, we highlighted the potential problems of using simple four-taxon tests to investigate patterns of homoeologous gene conversion in established allopolyploids.