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Diallel, line × tester (North Carolina Design-II) and simplified triple test-cross designs for the genetic analysis of a population of pure-breeding lines have been examined in respect of their ability to provide unbiased genetic estimates in the presence of non-allelic interactions and inequality of allelic frequencies. Simulations based on a two-locus genetic model showed that the estimates from different designs were differentially biased and the minimum biases were observed for the estimates obtained from the simplified triple test-cross analysis where the average degree of dominance is unaffected by the biases caused in the rather simple situations studied. Experimental results from a 10 males x 6 females factorial mating in wheat revealed that the non-allelic interactions had little effect on the magnitude of the additive component but the dominance component was upwardly biased. Both simulations and experimental results favoured the use of simplified triple test-cross design.