The symmetrization of radiation inside an indirectly driven axially symmetric target with two converters and an ellipsoidal casing is studied with the model of Murakami and Meyer-ter-Vehn, but with more realistic assumptions for the geometry. It is shown that with a useful value for the radius of the cylindrical converters, which transform beam energy into thermal radiation, it becomes much more difficult to achieve the required symmetrization, and this was not possible by varying the converter positions and radii