During rapid serial visual presentation (RSVP), two streams of letters simultaneously presented in the left and right visual fields (LVF and RVF) evoke visual potentials (VEPs) of EEG a few milliseconds earlier at the right (RH) than the left hemisphere (LH). This small LH VEP lag might be attributed to a RH advantage in initial processing of rapidly changing stimuli or to larger load of the LH by its specialized processing of letters from both visual fields simultaneously. In the present study, the two-stream condition was compared in two experiments to conditions with smaller instantaneous verbal load, namely with stimuli presented either solely or slightly earlier in the LVF or RVF. The RH advantage hypothesis predicts a LH VEP lag very similar to the standard two-stream condition when comparing between LH and RH VEPs contralateral to the single or earlier stream. The LH load hypothesis predicts shorter VEP latencies at the LH in the one-stream and earlier-stream than in the two-stream condition, resulting in an absent LH lag in those conditions. Results tended to be more in line with these latter predictions suggesting that in RSVP the LH might be more involved in partial processing of letters in search for target features. However, since the RH advantage hypothesis could not be reliably rejected these results might indicate a complex interplay between both hemispheres. This interplay would exploit the abilities of either hemisphere during the demanding processing of rapidly presented letters, both the LH advantage in letter processing and the RH advantage in visual perception at initial stages.