The relationship between fluid intelligence and working memory is of fundamental importance to understanding how capacity-limited structures such as working memory interact with inference abilities to determine intelligent behavior. Recent evidence has suggested that the relationship between a fluid abilities test, Raven's Progressive Matrices, and working memory capacity (WMC) may be invariant across difficulty levels of the Raven's items. We show that this invariance can only be observed if the overall correlation between Raven's and WMC is low. Simulations of Raven's performance revealed that as the overall correlation between Raven's and WMC increases, the item-wise point bi-serial correlations involving WMC are no longer constant but increase considerably with item difficulty. The simulation results were confirmed by two studies that used a composite measure of WMC, which yielded a higher correlation between WMC and Raven's than reported in previous studies. As expected, with the higher overall correlation, there was a significant positive relationship between Raven's item difficulty and the extent of the item-wise correlation with WMC. © 2014 Little, Lewandowsky and Craig.