E-Z Reader achieves an impressive fit of empirical eye movement data by simulating core processes of reading in a computational approach that includes serial word processing, shifts of attention, and temporal overlap in the programming of saccades. However, when common assumptions for the time requirements of these processes are taken into account, severe constraints on the time line within which these elements can be combined become obvious. We argue that it appears difficult to accommodate these processes within a largely sequential modeling framework such as E-Z Reader.