Whole-genome duplication (WGD) is central to the evolution of many eukaryotic genomes, in particular rendering angiosperm (flowering plant) genomes much less stable than those of animals. Following repeated duplication/triplication(s), angiosperm chromosome numbers have usually been restored to a narrow range, as one element in a 'diploidization' process that re-establishes diploid heredity. In several angiosperms affected by WGD, we show that chromosome number reduction (CNR) is best explained by intra- and/or inter-chromosomal crossovers to form new chromosomes that utilize the existing telomeres of 'invaded' and centromeres of 'invading' chromosomes, the alternative centromeres and telomeres being lost. Comparison with the banana (Musa acuminata) genome supports a 'fusion model' for the evolution of rice (Oryza sativa) chromosomes 2 and 3, implying that the grass common ancestor had seven chromosomes rather than the five implied by a 'fission model.' The 'invading' and 'invaded' chromosomes are frequently homoeologs, originating from duplication of a common ancestral chromosome and with greater-than-average DNA-level correspondence to one another. Telomere-centric CNR following recursive WGD in plants is also important in mammals and yeast, and may be a general mechanism of restoring small linear chromosome numbers in higher eukaryotes.