Past research indicates that specific shape recognition and spatial-relations encoding rely on subsystems that exhibit right-hemisphere advantages, whereas abstract shape recognition and spatial-relations encoding rely on subsystems that exhibit left-hemisphere advantages. Given these apparent regularities, we tested whether asymmetries in shape processing are causally related to asymmetries in spatial-relations processing. We examined performance in four tasks using the same stimuli with divided-visual-field presentations. Importantly, the asymmetry observed in any one task did not correlate with the asymmetries observed in the other tasks in ways predicted by extant theories. Asymmetries in shape processing and spatial-relations encoding may not be due to a common causal force influencing multiple subsystems.