Observers indicated whether a single probe letter presented to the left visual field/right hemisphere (LVF-RH) or to the right visual field/left hemisphere (RVF-LH) matched one of two, three, four, or five set letters in both name and case. For positive trials during the initial experimental session, the slope of the linear memory set size reaction time function was increased by perceptually degrading the probe letter on LVF-RH trials, but not on RVF-LH trials. In addition, perceptual degradation of the probe letter increased the intercept of the memory set size function more on RVF-LH trials than on LVF-RH trials. During subsequent experimental sessions, the same pattern of intercept results was obtained but perceptual degradation of the probe no longer changed the slope for either LVF-RH or RVF-LH trials. However, the slopes were uniformly lower on RVF-LH trials than on LVF-RH trials. The major results are consistent with hypothesized right-hemisphere efficiency for early processing stages and left-hemisphere efficiency for serial processing of alphanumeric information. The results further illustrate the importance of separating stages of processing in studies of cerebral laterality and indicate that the relative difficulty of the various stages can be a determinant of laterality results.