In the present experiments, the question being addressed was whether switching attention between perceptual dimensions and selective attention to dimensions are processes that compete over a common resource? Attention to perceptual dimensions is usually studied by requiring participants to ignore a never-relevant dimension. Selection failure (Garner's Interference, GI) is indicated by poorer performance in the filtering condition (when this dimension varies) as compared with baseline (when it is fixed). Switching between perceptual dimensions is usually studied with the task switching paradigm. In the present experiments, attention switching was manipulated by using single-task blocks and blocks in which participants switched between tasks or dimensions in reaction to task cues, and attention to dimensions was assessed by including a third, never-relevant dimension that was either fixed or varied randomly. In Experiments 1 (long cue-target interval, CTI) and 2 (short CTI), the tasks involved shape and color and the never-relevant dimension (texture) was chosen to be separable from them. In Experiments 3 (long CTI) and 4 (short CTI), the tasks involved shape and brightness and the never-relevant dimension, saturation, was chosen to be separable from shape and integral with brightness. Task switching did not generate GI but a short CTI did. Thus, switching and filtering generally do not compete over central limited resources unless under tight time pressure. Experiment 3 shows GI in the brightness task but not in the shape task, suggesting that participants switched their attention between brightness and shape when they switched tasks. (Contains 2 figures and 2 footnotes.)