Voice conversion systems have become increasingly important as the use of voice technology grows. Deep learning techniques, specifically generative adversarial networks (GANs), have enabled significant progress in the creation of synthetic media, including the field of speech synthesis. One of the most recent examples, StarGAN-VC, uses a single pair of generator and discriminator to convert voices between multiple speakers. However, the training stability of GANs can be an issue. The Top-K methodology, which trains the generator using only the best K generated samples that “fool” the discriminator, has been applied to image tasks and simple GAN architectures. In this work, we demonstrate that the Top-K methodology can improve the quality and stability of converted voices in a state-of-the-art voice conversion system like StarGAN-VC. We also explore the optimal time to implement the Top-K methodology and how to reduce the value of K during training. Through both quantitative and qualitative studies, it was found that the Top-K methodology leads to quicker convergence and better conversion quality compared to regular or vanilla training. In addition, human listeners perceived the samples generated using Top-K as more natural and were more likely to believe that they were produced by a human speaker. The results of this study demonstrate that the Top-K methodology can effectively improve the performance of deep learning-based voice conversion systems.