There is an ongoing debate about whether fixation durations during reading are only influenced by the processing difficulty of the words being fixated (i.e., the serial-attention hypothesis) or whether they are also influenced by the processing difficulty of the previous and/or upcoming words (i.e., the attention-gradient hypothesis). This article reports the results of 3 simulations that examine how systematic and random errors in the measurement of fixation locations can generate 2 phenomena that support the attention-gradient hypothesis: parafoveal-on-foveal effects and large spillover effects. These simulations demonstrate how measurement error can produce these effects within the context of a computational model of eye-movement control during reading (E-Z Reader; Reichle, 2011) that instantiates strictly serial allocation of attention, thus demonstrating that these effects do not necessarily provide strong evidence against the serial-attention hypothesis.