  We introduce a new Symanzik improved action by adding a 2x2 plaquette in such
a way that the Feynman rules in the covariant gauge simplify. We call this the
square Symanzik action. Some comparisons with the continuum and the standard
Wilson action are made in intermediate volumes, where mass ratios are
accurately known and the precise amount of improvement can be determined.
Ratios of the Lambda parameters will be presented, as well as partial results
for the one-loop improvement coefficients. We discuss some of the intricacies
that arise because of violations of unitarity at the scale of the cutoff. In
particular we show how a field redefinition in the zero-momentum effective
action allows one to remove scaling violations linear in the lattice spacing.
