''concave'' downward property of the standard static <q(q)over bar> po
tentials leads to the energy level inequalities E(n+2) - E(n+1) < E(n1) - E(n) in the quarkonium mass spectrum. However, this inequality is
experimentally observed to be reversed for n = 2 in charmonium and n
= 3 in bottomonium, a fact that is inexplicable in terms of any known
concave downward potential. We attempt to explain this by allowing for
the violation of the concavity condition in a small interval, i.e., a
''wrinkle'' in some recently proposed quarkonium potentials.