There is converging evidence, from various independent areas of neuroscience, for a functional specialization of the left and right cerebral hemispheres for positive and negative emotions, respectively ("valence theory" of emotional processing). One subfield, however, has produced mixed results, i.e. work on the detection of parafoveally presented positively or negatively emotional words by healthy subjects. Right or left visual field advantages were described and interpreted as reflecting the superiority of either the left hemisphere (LH) for linguistic material, or of the right hemisphere (RH) for highly emotional stimuli. Here we show that 48 healthy, right-handed participants' performance on a lateralized lexical decision task depends on their individual inclination to bisect a line to the left or right of the objective center. Only those with a bisection bias to the right showed the LH advantage for word detection known from the neuropsychological literature. Negative emotional words were processed with comparable accuracy in the two visual fields. However, a recognition advantage for negative over positive emotional words was found exclusively for those participants with a leftward line bisection bias. These results suggest that in work on functional hemispheric differences state variables like stimulus lateralization and word emotionality may be less decisive than the trait variable of lateral hemispatial attention. We propose a cautious reconsideration of the concept of "hemisphericity," which once emphasized individual differences in baseline hemispheric arousal, but was later dismissed in a reaction to oversimplifications in popular science accounts.