3D Gaussian Splatting (3DGS) has shown impressive results in real-time novel view synthesis. However, it often struggles under sparse-view settings, producing undesirable artifacts such as floaters, inaccurate geometry, and overfitting due to limited observations. We find that a key contributing factor is uncontrolled densification, where adding Gaussian primitives rapidly without guidance can harm geometry and cause artifacts. We propose AD-GS, a novel alternating densification framework that interleaves high and low densification phases. During high densification, the model densifies aggressively, followed by photometric loss based training to capture fine-grained scene details. Low densification then primarily involves aggressive opacity pruning of Gaussians followed by regularizing their geometry through pseudo-view consistency and edge-aware depth smoothness. This alternating approach helps reduce overfitting by carefully controlling model capacity growth while progressively refining the scene representation. Extensive experiments on challenging datasets demonstrate that AD-GS significantly improves rendering quality and geometric consistency compared to existing methods. The source code for our model can be found on our project page: https://gurutvapatle.github.io/publications/2025/ADGS.html.