Task inhibition is considered to facilitate switching to a new task and is assumed to decay slowly over time. Hence, more persisting inhibition needs to be overcome when returning to a task after one intermediary trial (ABA task sequence) than when returning after two or more intermediary trials (CBA task sequence). Schuch and Grange (J Exp Psychol Learn Mem Cogn 41:760–767, 2015) put forward the hypothesis that there is higher task conflict in ABA than CBA sequences, leading to increased cognitive control in the subsequent trial. They provided evidence that performance is better in trials following ABA than following CBA task sequences. Here, this effect of the previous task sequence (“N-3 effect”) is further investigated by varying the cue–stimulus interval (CSI), allowing for short (100 ms) or long (900 ms) preparation time for the upcoming task. If increased cognitive control after ABA involves a better preparation for the upcoming task, the N-3 effect should be larger with long than short CSI. The results clearly show that this is not the case. In Experiment 1, the N-3 effect was smaller with long than short CSI; in Experiment 2, the N-3 effect was not affected by CSI. Diffusion model analysis confirmed previous results in the literature (regarding the effect of CSI and of the ABA–CBA difference); however, the N-3 effect was not unequivocally associated with any of the diffusion model parameters. In exploratory analysis, we also tested the alternative hypothesis that the N-3 effect involves more effective task shielding, which would be reflected in reduced congruency effects in trials following ABA, relative to trials following CBA; congruency effects did not differ between these conditions. Taken together, we can rule out two potential explanations of the N-3 effect: Neither is this effect due to enhanced task preparation, nor to more effective task shielding.