As more and more personal photos are shared and tagged in social media, avoiding privacy risks such as unintended recognition, becomes increasingly challenging. We propose a new hybrid approach to obfuscate identities in photos by head replacement. Our approach combines state of the art parametric face synthesis with latest advances in Generative Adversarial Networks (GAN) for data-driven image synthesis. On the one hand, the parametric part of our method gives us control over the facial parameters and allows for explicit manipulation of the identity. On the other hand, the data-driven aspects allow for adding fine details and overall realism as well as seamless blending into the scene context. In our experiments we show highly realistic output of our system that improves over the previous state of the art in obfuscation rate while preserving a higher similarity to the original image content.