Three experiments explore aspects of the dissociable neural subsystems theory of hemispheric specialisation proposed by Marsolek and colleagues, and in particular a study by [Deason, R. G., & Marsolek, C. J. (2005). A critical boundary to the left-hemisphere advantage in word processing. "Brain and Language," 92, 251-261]. Experiment 1A showed that shorter exposure durations for lower-case words (13 ms) are associated with reduced right visual field (RVF) advantages compared with longer exposure durations (144 ms). Experiment 1B compared report accuracy for lower case and mixed case words at the same exposure duration (144 ms). The RVF advantage was reduced for mixed case words due to case alternation having more of an adverse effect in the RVF than in the LVF. Experiment 2 tested a different prediction of dissociable neural subsystems theory. Four-letter words were presented in mixed case in the LVF or RVF for 100 ms. They were preceded at the same location by a prime which could be in the same word in the same alternation pattern (e.g., FlAg-FlAg), the same word in the opposite alternation pattern (e.g., fLaG-FlAg), or an unrelated letter string in the same or opposite case alternation pattern (WoPk-FlAg or wOpK-FlAg). Relative to performance in the letter string prime conditions, which did not differ significantly between the two visual fields, there was more of an effect of word primes in the RVF than in the LVF. Importantly, the benefit of a word prime was the same whether the prime was in the same alternation pattern or was in the opposition alternation pattern. We argue that these results run contrary to the predictions of dissociable neural subsystems theory and are more compatible with theories which propose that a left hemisphere word recognition system is responsible for identifying written words, whether they are presented in the LVF or the RVF, and that letters are processed to an abstract graphemic level of representation before being identified by that system.