[en] Within the mode-coupling theory for the evolution of structural relaxation, the A₄-glass-transition singularities are identified for systems of particles interacting with a hard-sphere repulsion complemented by different short-ranged potentials: Baxter's singular potential regularized by a large-wavevector cut-off, a model for the Asakura-Oosawa depletion attraction, a triangular potential, a Yukawa attraction, and a square-well potential. The regular potentials yield critical packing fractions, critical Debye-Waller factors, and critical amplitudes very close to each other. The elastic moduli and the particle localization lengths for corresponding states of the Yukawa system and the square-well system may differ by up to 20 and 10%, respectively