  We derive an O(a^4)-improved lattice version of the continuum field-strength
tensor. Discretization errors are reduced via the combination of several clover
terms of various sizes, complemented by tadpole improvement. The resulting
improved field-strength tensor is used to construct O(a^4)-improved topological
charge and action operators. We compare the values attained by these operators
as we cool several configurations to self-duality with a previously defined
highly-improved action and assess the relative scale of the remaining
discretization errors.
