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Significance: Signal contamination is a major hurdle in functional near-infrared spectroscopy (fNIRS) of the human head as the NIR signal is contaminated with the changes corresponding to superficial tissue, therefore occluding the functional information originating from the cerebral region. For continuous wave, this is generally handled through linear regression of the shortest source-detector (SD) distance intensity measurement from all of the signals. Although phase measurements utilizing frequency domain (FD) provide deeper tissue sampling, the use of the shortest SD distance phase measurement for regression of superficial signal contamination can lead to misleading results, therefore suppressing cortical signals. Aim: An approach for FD fNIRS that utilizes a short-separation intensity signal directly to regress both intensity and phase measurements, providing a better regression of superficial signal contamination from both data-types, is proposed. Approach: Simulated data from realistic models of the human head are used, and signal regression using both intensity and phase-based components of the FD fNIRS is evaluated. Results: Intensity-based phase regression achieves a suppression of superficial signal contamination by 68% whereas phase-based phase regression is only by 13%. Phase-based phase regression is also shown to generate false-positive signals from the cortex, which are not desirable. Conclusions: Intensity-based phase regression provides a better methodology for minimizing superficial signal contamination in FD fNIRS., (© 2021 The Authors.)