  We describe and test a nonperturbatively improved single-plaquette lattice
action for 4-d SU(2) and SU(3) pure gauge theory, which suppresses large
fluctuations of the plaquette, without requiring the naive continuum limit for
smooth fields. We tune the action parameters based on torelon masses in
moderate cubic physical volumes, and investigate the size of cut-off effects in
other physical quantities, including torelon masses in asymmetric spatial
volumes, the static quark potential, and gradient flow observables. In 2-d O(N)
models similarly constructed nearest-neighbor actions have led to a drastic
reduction of cut-off effects, down to the permille level, in a wide variety of
physical quantities. In the gauge theories, we find significant reduction of
lattice artifacts, and for some observables, the coarsest lattice result is
very close to the continuum value. We estimate an improvement factor of 40
compared to using the Wilson gauge action to achieve the same statistical
accuracy and suppression of cut-off effects. The simplicity of the gauge action
makes it amenable for dynamical fermion simulations.
