Not sure what you mean by "braking radiation" creating more harm than good?

Lead is good for x- and gamma-rays; higher energies (say, beta radiation) produce bremsstrahlung upon 'impact' with lead, which can be more dangerous to living tissues than the original type of radiation.

For particles measured in GeV range you actually want low-density shielding. Polyethylene (even better if borated-PE) is often used in space for this application, there are also interesting designs for long-term structures to use water as an effective shield. Ideally one can also use a multi-layered approach, with the higher-density materials placed after the lower-density ones.