Head motion can be estimated at any point of fMRI image processing. Processing steps involving temporal interpolation (e.g., slice time correction or outlier replacement) often precede motion estimation in the literature. From first principles it can be anticipated that temporal interpolation will alter head motion in a scan. Here we demonstrate this effect and its consequences in five large fMRI datasets. Estimated head motion was reduced by 10-50% or more following temporal interpolation, and reductions were often visible to the naked eye. Such reductions make the data seem to be of improved quality. Such reductions also degrade the sensitivity of analyses aimed at detecting motion-related artifact and can cause a dataset with artifact to falsely appear artifact-free. These reduced motion estimates will be particularly problematic for studies needing estimates of motion in time, such as studies of dynamics. Based on these findings, it is sensible to obtain motion estimates prior to any image processing (regardless of subsequent processing steps and the actual timing of motion correction procedures, which need not be changed). We also find that outlier replacement procedures change signals almost entirely during times of motion and therefore have notable similarities to motion-targeting censoring strategies (which withhold or replace signals entirely during times of motion).