Using a relatively simple static model and allowing a number of additional radiation shields in an axially symmetric hohlraum having two converters, a systematic process of reducing the asymmetry of the radiation field on a fusion capsule is presented. As a result of this procedure, a hohlraum target is obtained that shows a high degree of symmetrization even in a very early stage of irradiation. The sensitivity of the symmetry to the form and the position of each hohlraum component is investigated. To increase the reliability of the results, an enhanced model of radiation reemission in a hohlraum target, including reemission of the converter, is developed. Using this enhanced model it is found that the obtained hohlraum configuration is still valid, while the simple reemission model leads to incorrect results in special cases. It is also shown that the detailed configuration of a hohlraum target, especially of the radiation shields, depends considerably on the temperature distribution of the converter surface, but it is always possible to achieve a high degree of symmetry with radiation shields.