In this work, an unusual approach is taken to calculate the ground state and first excited state energies of the anharmonic oscillator potential. By using the variational method, analytical wave functions which have extremely accurate expectation values for the quartic or sextic oscillators are obtained. The corrections due to the other terms are then calculated perturbatively. It is shown that each approach, which starts with a different choice of zeroth‐order term, provides results that agree with those computed from numerical integration and series solution. Joining the above schemes, yields a combined variational and perturbative treatment of anharmonic oscillator problems.