The behaviour of wheat cultivars in environments with different yield level and the progress of wheat breeding in Israel were investigated by a statistical exploration of 353 Regional Wheat Trials, performed from 1970 to 2002. In the trials 125 experimental and commercial cultivars of Triticum aestivum, 11 of T. durum and one Triticale line (summarised as cultivars) were tested. The yield levels of trials ranged from 0.5 to 8.8 t/ha. The assumption of additive cultivar effects did not fit to trials differing much in yield since genetic variance within trials was closely related to the yield level of trials. The cultivars differed in grain yield by multiplicative factors that were well reproducible and highly correlated across environments. The best differentiation of cultivars, expressed as the ratio of genetic to residual variance, was found in high yielding environments. Specific adaptations of cultivars to the environmental yield level were absent or negligible and the ranking of the tested cultivars was very similar across environments. Residual variance was very low after standardisation to equal genetic variance. Statistical cultivar × environment interactions might be largely artefacts of additive yield models, applied to non-standardised data. Significant differences between cultivars were observed in relative yield, stability of relative yield, earliness, height, kernel size and hectoliter weight. Cultivar yield was significantly associated with lodging resistance, short straw and low protein content, while the association with other traits was low or non-significant. Breeding resulted in an increase of the average relative yield of cultivars in regional trials by more than 30%. The top recent bread wheat cultivar Galil is yielding approximately twice more than cv. Florence Aurore, the leading cultivar till the seventies. Breeding progress for yield was fast in the seventies, but only moderate in the last 10 years, with cv. Galil as the top yielder since 1996. Further breeding progress might be harder to achieve than in the past.