Multivoxel pattern analysis (MVPA) typically begins with the estimation of single trial activation levels, and several studies have examined how different procedures for estimating single trial activity affect the ultimate classification accuracy of MVPA. Here we show that the currently preferred estimation procedures impart spurious positive correlations between the means of different category activity estimates within the same scanner run. In other words, if the mean of the estimates for one type of trials is high (low) in a given scanner run, then the mean of the other type of trials is also high (low) for that same scanner run, and the run-level mean across all trials therefore shifts from run to run. Simulations show that these correlations occur whenever there is a need to deconvolve overlapping trial activities in the presence of noise. We show that subtracting each voxel's run-level mean across all trials from all the estimates within that run (i.e., run-level mean centering of estimates), by cancelling out these mean shifts, leads to robust and significant improvements in MVPA classification accuracy. These improvements are seen in both simulated and real data across a wide variety of situations. However, we also point out that there could be cases when mean activations are expected to shift across runs and that run-level mean centering could be detrimental in some of these cases (e.g., different proportion of trial types between different runs).