Methods of adjustment for two-dimensional spatial heterogeneity of grain yield were investigated for 224 UK cereal trials. The methods used row and column ‘block’ analysis of plot yields and neighbour analysis based on first differences of plot yields. In 36% of trial analyses for block models and 30% for neighbour models the average variance of variety differences was reduced by more than 10% compared with the better of the one-dimensional row or column models. Compared with complete blocks, 2-D block analysis had a mean efficiency of 153% whereas the conventional 1-D block analysis (by rows) had a mean efficiency of 127%. Similarly, 2-D neighbour analysis had a mean efficiency of 159% whereas the 1-D analysis had a mean efficiency of 137%. Recently, general statistical methods have been developed for two-dimensional design and analysis; their wider use should lead to major gains in the precision of variety trials.