We consider the effect that a finitely conducting inner core may have on the dynamo processes in the outer core. Because a finitely conducting inner core has a diffusive timescale of its own of a few thousand years, which is long compared with the most rapid advective timescales possible in the outer core, the field in the inner core must necessarily average over these very rapid timescales. This averaging-out may then have a stabilizing influence, preventing the very rapid timescales from dominating the dynamo processes in the outer core. In this work we present a solution to the mean-field geodynamo equations which seems to exhibit these features. In this way it may be possible to reconcile the complicated, time-dependent nature of the field and flow in the dynamically active portion of the outer core with the simple, relatively stable nature of the externally observed dipole component of the Earth's magnetic field.