A variety of preprocessing techniques are available to correct subject-dependant artifacts in fMRI, caused by head motion and physiological noise. Although it has been established that the chosen preprocessing steps (or "pipeline") may significantly affect fMRI results, it is not well understood how preprocessing choices interact with other parts of the fMRI experimental design. In this study, we examine how two experimental factors interact with preprocessing: between-subject heterogeneity, and strength of task contrast. Two levels of cognitive contrast were examined in an fMRI adaptation of the Trail-Making Test, with data from young, healthy adults. The importance of standard preprocessing with motion correction, physiological noise correction, motion parameter regression and temporal detrending were examined for the two task contrasts. We also tested subspace estimation using Principal Component Analysis (PCA), and Independent Component Analysis (ICA). Results were obtained for Penalized Discriminant Analysis, and model performance quantified with reproducibility (R) and prediction metrics (P). Simulation methods were also used to test for potential biases from individual-subject optimization. Our results demonstrate that (1) individual pipeline optimization is not significantly more biased than fixed preprocessing. In addition, (2) when applying a fixed pipeline across all subjects, the task contrast significantly affects pipeline performance; in particular, the effects of PCA and ICA models vary with contrast, and are not by themselves optimal preprocessing steps. Also, (3) selecting the optimal pipeline for each subject improves within-subject (P,R) and between-subject overlap, with the weaker cognitive contrast being more sensitive to pipeline optimization. These results demonstrate that sensitivity of fMRI results is influenced not only by preprocessing choices, but also by interactions with other experimental design factors. This paper outlines a quantitative procedure to denoise data that would otherwise be discarded due to artifact; this is particularly relevant for weak signal contrasts in single-subject, small-sample and clinical datasets.