The identification of resting state networks (RSNs) and the quantification of their functional connectivity in resting-state fMRI (rfMRI) are seriously hindered by the presence of artefacts, many of which overlap spatially or spectrally with RSNs. Moreover, recent developments in fMRI acquisition yield data with higher spatial and temporal resolutions, but may increase artefacts both spatially and/or temporally. Hence the correct identification and removal of non-neural fluctuations is crucial, especially in accelerated acquisitions. In this paper we investigate the effectiveness of three data-driven cleaning procedures, compare standard against higher (spatial and temporal) resolution accelerated fMRI acquisitions, and investigate the combined effect of different acquisitions and different cleanup approaches. We applied single-subject independent component analysis (ICA), followed by automatic component classification with FMRIB's ICA-based X-noiseifier (FIX) to identify artefactual components. We then compared two first-level (within-subject) cleaning approaches for removing those artefacts and motion-related fluctuations from the data. The effectiveness of the cleaning procedures was assessed using time series (amplitude and spectra), network matrix and spatial map analyses. For time series and network analyses we also tested the effect of a second-level cleaning (informed by group-level analysis). Comparing these approaches, the preferable balance between noise removal and signal loss was achieved by regressing out of the data the full space of motion-related fluctuations and only the unique variance of the artefactual ICA components. Using similar analyses, we also investigated the effects of different cleaning approaches on data from different acquisition sequences. With the optimal cleaning procedures, functional connectivity results from accelerated data were statistically comparable or significantly better than the standard (unaccelerated) acquisition, and, crucially, with higher spatial and temporal resolution. Moreover, we were able to perform higher dimensionality ICA decompositions with the accelerated data, which is very valuable for detailed network analyses.