A Strömgren sphere is the theoretical result of an ionizing source such as a hot star placed in a uniform medium such as neutral atomic hydrogen. The steady state solution which balances ionizations and recombinations results in a sphere of ionized hydrogen centered on the star. We have extended the model to allow for an evacuated, spherical cavity either centered on the star or with the star displaced with respect to the evacuated cavity. The resulting brightness distributions of a few representative geometries are illustrated and compared to actual H II regions of the Large Magellanic Cloud and the Milky Way. The extra degrees of freedom provided by our model allow it to approximate the actual H II regions better than a classic Strömgren sphere. Possible mechanisms to create the evacuated cavity are winds or supernovae.