Many modern online 3D applications and videogames rely on parametric models of human faces for creating believable avatars. However, manual reproduction of someone's facial likeness with a parametric model is difficult and time-consuming. Machine Learning solution for that task is highly desirable but is also challenging. The paper proposes a novel approach to the so-called Face-to-Parameters problem (F2P for short), aiming to reconstruct a parametric face from a single image. The proposed method utilizes synthetic data, domain decomposition, and domain adaptation for addressing multifaceted challenges in solving the F2P. The open-sourced codebase illustrates our key observations and provides means for quantitative evaluation. The presented approach proves practical in an industrial application; it improves accuracy and allows for more efficient models training. The techniques have the potential to extend to other types of parametric models.