The Slotted-Hidden-Gap (SHG) connection is an improved version of the conventional welded tube-togusset connection between hollow braces and framing elements used in Concentrically Braced Frames (CBFs), offering an enhanced performance without the need for additional reinforcement. Previous studies have demonstrated the efficiency of this feature in circular and square Hollow Structural Section (HSS) braces under monotonic tensile loading conditions, leading to the development of a design methodology based on the CSA S16-19 to construct the connection. However, limited research has been dedicated to investigating the compressive behavior of the brace and its connections. In order to obtain a more comprehensive understanding of the seismic behavior of the SHG connection, a numerical parametric study is conducted to examine the inelastic response of the connection under reversed cyclic loading conditions. Various parameters are considered, including the square HSS tube’s size, the weld’s length and size, the brace’s slenderness, and the degree of confinement of the gusset plate that plays a crucial role in the development of a plastic hinge. Designed based on the previously developed methodology, the simulated braces demonstrated their ability to withstand compression cycles without fracturing at the connection, making it capacity design protected. The findings indicate that all confinement degrees of the gusset plate in the numerically tested models, from a constrained gusset plate to a linear clearance, led to a fracture away from the connection at mid-length of the brace. Notably, the use of a constrained gusset plate that redirected the moment towards the HSS tube’s end resulted in an average additional 2.85% of plastic strains at the brace’s slots compared to an elliptical or linear offset in the gusset plate. This effect was observed in stockier braces, yet no fracturing occurred.