Conventional buckling braces are the most commonly used steel bracing systems but are characterized by intense local midlength buckling that leads to unstable energy dissipation and finally fracture. Moreover, they are unable to dissipate energy in the event of low-level earthquakes and provide limited post-yielding stiffness. The present paper proposes a prototype design of conventional buckling braces with improved seismic performance by introducing eccentricity along the brace length. Steel braces with intentional eccentricity (BIE) are deformed by small story drift. The inherent moment caused by eccentricity affects their response, and the braces display trilinear behavior under tension and transition smoothly to post-buckling behavior under compression. Owing to the moment contribution, stresses and strains are uniformly distributed along the brace length, delaying local buckling concentration, and, thus, the member’s life is appreciably extended. The present experimental work on BIEs reveals that the braces offer a reduced stiffness up to 56% on the initial stiffness maintaining the same strength with the corresponding conventional brace, provide large tensile post-yielding stiffness of 14–18% of the initial stiffness, stably dissipate energy during cyclic loading, and delay local buckling and fracture until large story drift levels (up to 2 and 4%, respectively).