The present paper continues a series of the authors’ studies on improving conventional concentrically braced frames (CBFs). In previous works, the authors equipped a CBF with a restrained local fuse to improve its behavior, thus introducing local fuse–auxiliary element concentric braces (LF-AECBs). The mechanism of LF-AECBs with a restricted fuse in the length increased the ductility and energy dissipation capacity of the bracing system by limiting the overall buckling locally to the compressive zone. However, further numerical studies suggested that due to early buckling, now local, the restrained local fuse could not be exploited until the failure. Therefore, this study introduces an improved local fuse–auxiliary element concentric brace (ILF-AECB) to fix the issue. Numerical studies are also done to determine the optimal shape of ILF-AECBs in order to obtain maximum energy dissipation capacity and ductility under cyclic loading. In this article, the results of experimental and numerical studies show that ILF-AECBs with a new formulation delaying the fuse buckling completely succeed in using the full capacity of the local fuse for energy dissipation and ductility. Moreover, the analytical study shows that the frame equipped with ILF-AECB offered much better performance in terms of energy dissipation and reduction of the input demand to the structural elements compared to the similar CBFs.