Genotype-environment interactions (GEI) are important in crop improvement if genotype ranks change over environments. Current tests for crossover (rank changing) interactions (COI) assume that effects are all fixed or all random. The objective of this presentation is to describe a new test for COI under the model with a mixture of fixed and random genotypic, environmental and GEI effects. The key part of this new test is the identification of predictable functions, the linear combinations of both best linear unbiased estimates (BLUEs) of fixed effects and best linear unbiased predictors (BLUPs) of random effects. The difference between a pair of genotypes at a random environment or the difference between a pair of environments for a random genotype is simply the difference between a pair of predictable functions. The predictable functions are used in the same way as the usual estimable functions for the fixed effects in hypothesis testing except that the BLUPs of random effects are adjusted (shrunken) by accounting for the uncertainty arising from the distributions of these effects. The procedure is used to analyze barley (Hordeum vulgare L.) cultivar trials. Results from the analyses show that the fixed-effect model treats random effects as unshrunken fixed effects and thus is more likely to detect COI than mixed- or random-effect models. Therefore, significant COI may be over-emphasized when random GEI effects are treated as fixed.