Sequences of reaction times (RT) produced by participants in an experiment are not only influenced by the stimuli, but by many other factors as well, including fatigue, attention, experience, IQ, handedness, etc. These confounding factors result in longterm effects (such as a participant’s overall reaction capability) and in short- and medium-time fluctuations in RTs (often referred to as ‘local speed effects’). Because stimuli are usually presented in a random sequence different for each participant, local speed effects affect the underlying ‘true’ RTs of specific trials in different ways across participants. To be able to focus statistical analysis on the effects of the cognitive process under study, it is necessary to reduce the effect of confounding factors as much as possible. In this paper we propose and compare techniques and criteria for doing so, with focus on reducing (‘filtering’) the local speed effects. We show that filtering matters substantially for the significance analyses of predictors in linear mixed effect regression models. The performance of filtering is assessed by the average between-participant correlation between filtered RT sequences and by Akaike’s Information Criterion, an important measure of the goodness-of-fit of linear mixed effect regression models.