In the Arabidopsis multiparent recombinant inbred line mapping population, a limited number of plants were detected that lacked axillary buds in most of the axils of the cauline (stem) leaves, but formed such buds in almost all rosette axils. Genetic analysis showed that polymorphisms in at least three loci together constitute this phenotype, which only occurs in late-flowering plants. Early flowering is epistatic to two of these loci, called REDUCED SHOOT BRANCHING1 (RSB1) and RSB2, which themselves do not affect flowering time. Map-based cloning and confirmation by transformation with genes from the region where RSB1 was identified by fine-mapping showed that a specific allele of AGAMOUS-Like6 from accession C24 conferred reduced branching in the cauline leaves. Site-directed mutagenesis in the Columbia allele revealed the causal amino acid substitution, which behaved as dominant negative, as was concluded from a loss-of-function mutation that showed the same phenotype in the late-flowering genetic background. This causal allele occurs at a frequency of 15% in the resequenced Arabidopsis thaliana accessions and correlated with reduced stem branching only in late-flowering accessions. The data show the importance of natural variation and epistatic interactions in revealing gene function.