fMRI is noisy and suffers from signal origin ambiguities. We propose a straightforward method that can classify the origin of neurally- and non-neurally-driven signal fluctuations by means of simultaneously acquired BOLD and CBV fMRI-data. For neurally-driven fMRI-signal fluctuations, BOLD and CBV are synchronized. For non-neurally-driven fluctuations, however, abnormal temporal correlations are seen. Upon identification of the non-neural components, they can be filtered out. This helps to remove artifacts and improve the specificity and interpretability of fMRI activation maps. Moreover, we show that it can remove venous signal components in ultra-high-resolution fMRI and improve the spatial specificity across cortical laminae.