In the spirit of recent work of Lamm, Malchiodi and Micallef in the setting of harmonic maps, we identify Yang-Mills connections obtained by approximations with respect to the Yang-Mills α- energy. More specifically, we show that for the SU(2) Hopf fibration over S4, for sufficiently small α values the SO(5, 1)-invariant ADHM instanton is the unique α-critical point which has Yang-Mills α-energy lower than a specific threshold.