The Australian Synchrotron Imaging and Medical Beamline (IMBL) uses a superconducting multipole wiggler (SCMPW) source, dual crystal Laue monochromator and 135 m propagation distance to enable imaging and computed tomography (CT) studies of large samples with mono-energetic radiation. This study aimed to quantify two methods for CT dose reduction: wiggler source operation at reduced magnetic field strength, and beam modulation with spatial filters placed upstream from the sample. Transmission measurements with copper were used to indirectly quantify the influence of third harmonic radiation. Operation at lower wiggler magnetic field strength reduces dose rates by an order of magnitude, and suppresses the influence of harmonic radiation, which is of significance near 30 keV. Beam shaping filters modulate the incident beam profile for near constant transmitted signal, and offer protection to radio-sensitive surface organs: the eye lens, thyroid and female breast. Their effect is to reduce the peripheral dose and the dose to the scanned volume by about 10% for biological samples of 35-50 mm diameter and by 20-30% for samples of up to 160 mm diameter. CT dosimetry results are presented as in-air measurements that are specific to the IMBL, and as ratios to in-air measurements that may be applied to other beamlines. As CT dose calculators for small animals are yet to be developed, results presented here and in a previous study may be used to estimate absorbed dose to organs near the surface and the isocentre.