Voice conversion for speaker anonymization is an emerging field in speech processing research. Many state-of-the-art approaches are based on the resynthesis of the phoneme posteriorgrams (PPG), the fundamental frequency (F0) of the input signal together with modified X-vectors. Our research focuses on the role of F0 for speaker anonymization, which is an understudied area. Utilizing the VoicePrivacy Challenge 2020 framework and its datasets we developed and evaluated eight low-complexity F0 modifications prior resynthesis. We found that modifying the F0 can improve speaker anonymization by as much as 8% with minor word-error rate degradation.