In the present paper, I review evidence for the universality of the global effect, i.e. the general tendency to move the eyes towards the centre of gravity of the peripheral configuration, and show that the effect is strongly constrained by the retinal location of the stimuli. First, stimuli that are displayed in a central foveal region of a 1-1.5 degrees radius fail to deviate the eyes in a centre-of-gravity manner; this is referred to as the foveal dead zone. Second, the stimuli that are too eccentric relative to the saccade target and/or the main stimulation site are filtered out. These limitations reflect physiological constraints and the dynamics of the patterns of activity in a visual saliency map. They form the basis for a low-level centre-of-gravity type account of eye guidance in natural perceptual tasks such as reading.