3D Gaussian Splatting is known for its realistic and efficient novel-view synthesis, but extracting high-quality surfaces from its point-based representation remains challenging. In this paper, we improve the infidelity of 3D Gaussian surface representation by introducing a scale regularizer to flatten the 3D Gaussians (FGauS) and pulling them closer to the surface. We also alleviate the issue of rotation-only updates in existing methods from the supervision of rendered 3D Gaussian normals by proposing a Depth-Normal regularizer that couples normals with geometric parameters for more complete updates. To reduce inconsistencies, we add a confidence term. Additionally, we employ a densification and splitting strategy to better control the size and distribution of Gaussians for accurate surface modeling. We further improve our FGauS by proposing FGauS-I that jointly optimizes an implicit radiance field and the fattened Gaussian Splatting to obtain detailed and complete surfaces. Experiments show that our method surpasses both implicit and explicit baselines in reconstruction quality, offers competitive appearance quality, trains faster, and renders at over 100 FPS. Our method remains effective even with 20% of training data due to our regularizers and normal priors.