This paper presents the experimental results of two welded unreinforced flange-welded web (WUF-W) beam-to-column connections that defy the current design paradigm of prequalified welded connections. The proposed WUF-W connections feature customized beveled backing bars that are intentionally left in place after the completion of the beam flange-to-column face complete joint penetration welds. The connection design aims at a stable hysteretic response by exploiting the beneficial aspects of appreciable panel zone shear yielding (i.e., inelastic shear distortions of at least 15γy, where γy is the panel zone shear distortion at yield), by considering a shear strength-to-demand ratio of 0.8. To prevent divot fracture in the column, minimum through-thickness toughness requirements were imposed for the steel column material. The experimental results suggest that the proposed WUF-W connections achieve a stable hysteretic response up until lateral drift demands of at least 7% rad, while a non-softening response was assured up to 9% rad. The beveled backing bars minimize the associated fracture potential near the beam web centerline, which is a primary concern in prequalified field welded moment connections when conventional weld backing bars are employed. The tests suggest that, under a symmetric cyclic loading protocol, local buckling near the steel beams is prevented up until a lateral drift demand of 6% rad, which is an important finding from structural repairability and stability standpoints. The ultimate failure modes of the welded connections, which are attributable to ductile crack initiation and propagation, are consistent regardless of the employed lateral loading histories, which involved standard symmetric cyclic and collapse-consistent loading protocols. The implications for the seismic design of steel moment resisting frames (MRFs) and the limitations of the present work are discussed.