An attempt has been made for the optimisation of the radiation shielding of a spacecraft design concept with inertial fusion energy propulsion for manned or heavy cargo deep space missions beyond earth orbit. Rocket propulsion is provided by fusion power deposited in the inertial confined fuel pellet debris, and with the help of a magnetic nozzle. The allowable nuclear heating in the super conducting magnet coils (up to 5 mW/cm(3)) is the crucial criterion for the dimensioning of the radiation shielding structure of the spacecraft. The optimized design reduced the shield mass from 600 tons to 93 and 88 tons with natural and enriched lithium, respectively. The space craft mass was 6000 tons. Total peak nuclear power density in the coils is calculated to be 5.0 mW/cm(3) for a fusion power of 17,500 MW. Peak neutron heating density is 2.6 mW/cm(3) and peak gamma -ray heating density is 2.9 mW/cm(3) (all on different points). However, volume averaged heat generation in the coils is much lower, namely 0.30, 0.73 and 1.03 mW/cm(3) for neutron, gamma -ray and total nuclear heating, respectively. (C) 2001 Elsevier Science Ltd. All rights reserved.