Most people are right-handed and left-cerebrally dominant for speech, leading historically to the general notion of left-hemispheric dominance, and more recently to genetic models proposing a single lateralizing gene. This hypothetical gene can account for higher incidence of right-handers in those with left cerebral dominance for speech. It remains unclear how this dominance relates to the right-cerebral dominance for some nonverbal functions such as spatial or emotional processing. Here we use functional magnetic resonance imaging with a sample of 155 subjects to measure asymmetrical activation induced by speech production in the frontal lobes, by face processing in the temporal lobes, and by spatial processing in the parietal lobes. Left-frontal, right-temporal, and right-parietal dominance were all intercorrelated, suggesting that right-cerebral biases may be at least in part complementary to the left-hemispheric dominance for language. However, handedness and parietal asymmetry for spatial processing were uncorrelated, implying independent lateralizing processes, one producing a leftward bias most closely associated with handedness, and the other a rightward bias most closely associated with spatial attention.