  In this sequel to Resolution except for minimal singularities I, we find the
smallest class of singularities in four variables with which we necessarily end
up if we resolve singularities except for normal crossings. The main new
feature is a characterization of singularities in four variables which occur as
limits of triple normal crossings singularities, and which cannot be eliminated
by a birational morphism that avoids blowing up normal crossings singularities.
