Scholars have argued that imprecise data graphics, specifically those displaying decorative dimensionality of data, may lead to inaccurate interpretations. Empirical tests of decorative dimensionality have produced mixed results. The literature also suggests that the effects of decorative dimensionality may depend on the cognitive demand of a given task. This study employs an experimental design in which participants receive three levels of decorative dimensionality amidst systematically varying levels of cognitive demand. Graph type and subject matter knowledge are controlled for by design. The hypothesis that the impact of decorative dimensionality on comprehension not only depends on the cognitive demand of the task at hand, but also on the user's graphical literacy, is tested. Results indicate that graphical literacy moderates the interaction between cognitive demand and decorative dimensionality. A familiarity effect may also be present during the display of common two-dimensional bars. (Contains 3 figures and 1 table.)