Independent component analysis (ICA) has been proven useful for suppression of artifacts in EEG recordings. It involves separation of measured signals into statistically independent components or sources, followed by rejection of those deemed artificial. We show that a "leak" of cerebral activity of interest into components marked as artificial means that one is going to lost that activity. To overcome this problem we propose a novel wavelet enhanced ICA method (wICA) that applies a wavelet thresholding not to the observed raw EEG but to the demixed independent components as an intermediate step. It allows recovering the neural activity present in "artificial" components. Employing semi-simulated and real EEG recordings we quantify the distortions of the cerebral part of EEGs introduced by the ICA and wICA artifact suppressions in the time and frequency domains. In the context of studying cortical circuitry we also evaluate spectral and partial spectral coherences over ICA/wICA-corrected EEGs. Our results suggest that ICA may lead to an underestimation of the neural power spectrum and to an overestimation of the coherence between different cortical sites. wICA artifact suppression preserves both spectral (amplitude) and coherence (phase) characteristics of the underlying neural activity.