  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 {\alpha}-energy. More specifically, we show that
for the SU(2) Hopf fibration over the four sphere, for sufficiently small
{\alpha} values the SO(4) invariant ADHM instanton is the unique
{\alpha}-critical point which has Yang-Mills {\alpha}-energy lower than a
specific threshold.
