We introduce a novel method to improve the performance of the VoicePrivacy Challenge 2022 baseline B1 variants. Among the known deficiencies of x-vector-based anonymization systems is the insufficient disentangling of the input features. In particular, the fundamental frequency (F0) trajectories, which are used for voice synthesis without any modifications. Especially in cross-gender conversion, this situation causes unnatural sounding voices, increases word error rates (WERs), and personal information leakage. Our submission overcomes this problem by synthesizing an F0 trajectory, which better harmonizes with the anonymized x-vector. We utilized a low-complexity deep neural network to estimate an appropriate F0 value per frame, using the linguistic content from the bottleneck features (BN) and the anonymized x-vector. Our approach results in a significantly improved anonymization system and increased naturalness of the synthesized voice. Consequently, our results suggest that F0 extraction is not required for voice anonymization.