This paper tackles GAN optimization and stability issues in the context of voice conversion. First, to simplify the conversion task, we propose to use spectral envelopes as inputs. Second we propose two adversarial weight training paradigms, the generalized weighted GAN and the generator impact GAN, both aim at reducing the impact of the generator on the discriminator, so both can learn more gradually and efficiently during training. Applying an energy constraint to the cycleGAN paradigm considerably improved conversion quality. A subjective experiment conducted on a voice conversion task on the voice conversion challenge 2018 dataset shows first that despite a significantly reduced network complexity, the proposed method achieves state-of-the-art results, and second that the proposed weighted GAN methods outperform a previously proposed one.