The pre-saccadic preview of a peripheral target enhances the efficiency of its post-saccadic processing, termed the extrafoveal preview effect. Peripheral visual performance -and thus the quality of the preview- varies around the visual field, even at iso-eccentric locations: it is better along the horizontal than vertical meridian and along the lower than upper vertical meridian. To investigate whether these polar angle asymmetries influence the preview effect, we asked human participants (to preview four tilted gratings at the cardinals, until a central cue indicated to which one to saccade. During the saccade, the target orientation either remained or slightly changed (valid/invalid preview). After saccade landing, participants discriminated the orientation of the (briefly presented) second grating. Stimulus contrast was titrated with adaptive staircases to assess visual performance. Expectedly, valid previews increased participants' post-saccadic contrast sensitivity. This preview benefit, however, was inversely related to polar angle perceptual asymmetries; largest at the upper, and smallest at the horizontal meridian. This finding reveals that the visual system compensates for peripheral asymmetries when integrating information across saccades, by selectively assigning higher weights to the less-well perceived preview information. Our study supports the recent line of evidence showing that perceptual dynamics around saccades vary with eye movement direction.