We report a “Double Decoy” experiment designed to separate two competing accounts of the asymmetric dominance effect. The experiment places an additional decoy alternative within the range of existing alternatives, which should leave choice behaviour unaltered if attributes are weighted by their range. Instead, we observe a decrease in the relative proportion of targets chosen, particularly for subjects who exhibited an initial decoy effect. We also observe considerably more variation in individual behaviour than expected. We therefore consider an alternative theory in which attributes values are compared with diminishing sensitivity (via divisive normalization) and assess its performance in an additional discrete choice experiment previously used in the discrete choice literature. We find that divisive normalization captures behaviour better than range normalization and the linear additive Logit model typically used in applied settings. We therefore propose divisive normalization as both a neuro-computational explanation for context effects and a useful empirical tool for applied researchers.