The impact of eddy potential vorticity fluxes on the dynamical evolution of the flow is obscured by the presence of large and dynamically-inert rotational fluxes. However, the decomposition of eddy potential vorticity fluxes into rotational and divergent components is non-unique in a bounded domain and requires the imposition of an additional boundary condition. Here it is proposed to invoke a one-to-one correspondence between divergent eddy potential vorticity fluxes and non-divergent eddy momentum tendencies in the quasi-geostrophic residual-mean equations in order to select a unique divergent eddy potential vorticity flux. The divergent eddy potential vorticity flux satisfies a zero tangential component boundary condition. In a simply connected domain, the resulting divergent eddy potential vorticity flux satisfies a powerful optimality condition: it is the horizontally oriented divergent flux with minimum L2 norm. Hence there is a well-defined sense in which this approach removes as much of the dynamically inactive eddy potential vorticity flux as possible, and extracts an underlying dynamically active divergent eddy potential vorticity flux. It is shown that this approach leads to a divergent eddy potential vorticity flux which has an intuitive physical interpretation, via a direct relationship to the resulting forcing of the mean circulation.