Possibilities for improving the performance of conventional 60 cm thick uniform composition Fe-H2O shields backed by a B4C layer are investigated. The maximum heating rate in the superconducting coils due to (1) Optimally distributing the Fe and H2O across the shield; (2) Optimally distributing the Fe, H2O and B4C; (3) Using TiH2 as the primary hydrogeneous material; (4) Using tungsten instead of iron; and (5) Using a tungsten-copper composite material instead of tungsten, is found to be, respectively, 1.6, 3.6, 6, 32 and 56 times lower than in the reference shield. The development and use of tungsten-, and TiH2-based composite materials for improving the performance and/or economical attractiveness of radiation shields is proposed.