3D Gaussian Splatting (GS) significantly struggles to accurately represent the underlying 3D scene geometry, resulting in inaccuracies and floating artifacts when rendering depth maps. In this paper, we address this limitation, undertaking a comprehensive analysis of the integration of depth priors throughout the optimization process of Gaussian primitives, and present a novel strategy for this purpose. This latter dynamically exploits depth cues from a readily available stereo network, processing virtual stereo pairs rendered by the GS model itself during training and achieving consistent self-improvement of the scene representation. Experimental results on three popular datasets, breaking ground as the first to assess depth accuracy for these models, validate our findings.