Polyploidy, which results from whole genome duplication (WGD), has shaped the long-term evolution of eukaryotic genomes in all kingdoms. Polyploidy is also implicated in adaptation, domestication, and speciation. Yet when WGD newly occurs, the resulting neopolyploids face numerous challenges. A particularly pernicious problem is the segregation of multiple chromosome copies in meiosis. Evolution can overcome this challenge, likely through modification of chromosome pairing and recombination to prevent deleterious multivalent chromosome associations, but the molecular basis of this remains mysterious. We study mechanisms underlying evolutionary stabilization of polyploid meiosis using Arabidopsis arenosa, a relative of A. thaliana with natural diploid and meiotically stable autotetraploid populations. Here we investigate the effects of ancestral (diploid) versus derived (tetraploid) alleles of two genes, ASY1 and ASY3, that were among several meiosis genes under selection in the tetraploid lineage. These genes encode interacting proteins critical for formation of meiotic chromosome axes, long linear multiprotein structures that form along sister chromatids in meiosis and are essential for recombination, chromosome segregation, and fertility. We show that derived alleles of both genes are associated with changes in meiosis, including reduced formation of multichromosome associations, reduced axis length, and a tendency to more rod-shaped bivalents in metaphase I. Thus, we conclude that ASY1 and ASY3 are components of a larger multigenic solution to polyploid meiosis in which individual genes have subtle effects. Our results are relevant for understanding polyploid evolution and more generally for understanding how meiotic traits can evolve when faced with challenges.