Accurate estimation of the temporal correlations that exist in fMRI time-series is essential in order to avoid a high false positive rate. A common approach is to pre-whiten data using an AR(1)+white noise model. However, this approach proves insufficient for repetition times (TR) <1.5s. An alternative is to expand the set of covariance components included in the model (of serial correlations), as in the “FAST” option implemented by SPM12. Here, we show that this model can be used to accurately pre-whiten rapidly sampled data, and identify an upper bound on the parameterisation (i.e., number of covariance components) that precludes numerical overflow with ill-conditioned matrices. Such a model is important given the increasing use of rapid imaging techniques, such as multiband imaging. Using this technique, 18 components provided robust results with TR times ranging from 0.35s to 2.8s.