Corkscrew domains satisfy a simple geometric condition that prevents narrow spikes in the boundary. Some examples include smooth domains, Lipschitz domains and rough domains such as the the von Koch snowflake. It is usually impossible to display a corkscrew domain locally as the area above a graph, even when the boundary has finite surface measure. In 1990 G. David and D. Jerison gave a geometric argument which shows that on a corkscrew domain if the surface measure is Ahlfors regular then the boundary contains big pieces of Lipschitz graphs. Their construction has the nice feature that the approximations lie inside the original domain, which allows applications to harmonic measure. In this talk, we will discuss two observations. First, surface measure on a corkscrew domain is automatically lower Ahlfors regular. Second, the assumption that surface measure be upper Ahlfors regular is not required to build David and Jerison's approximations. As an application, we obtain a partial analogue of the F. and M. Riesz Theorem: on an NTA domain with finite surface measure, every set of vanishing harmonic measure has zero Hausdorff measure.