  As an application of perfect lattice perturbation theory, we construct an
O(\lambda) perfect lattice action for the anharmonic oscillator analytically in
momentum space. In coordinate space we obtain a set of 2-spin and 4-spin
couplings \propto \lambda, which we evaluate for various masses. These
couplings never involve variables separated by more than two lattice spacings.
The O(\lambda) perfect action is simulated and compared to the standard action.
We discuss the improvement for the first two energy gaps \Delta E_1, \Delta E_2
and for the scaling quantity \Delta E_2 / \Delta E1 in different regimes of the
interaction parameter, and of the correlation length.
