The use of Computerised microtomography (CμT) in biomedical research is well established, with most applications developed at synchrotron facilities. The possibility to non-invasively monitor morphological changes in biological samples, makes it an attractive technique in biomedicine. However, high absorbed doses and long examination times are a disadvantage that limits the possibilities of performing longitudinal examinations. The aim of this work was to optimise CmT using conventional X-ray tubes for applications in non-destructive material testing and for skeleton research in small animals (rat). A calculational model of the imaging system was developed and used to optimise the relation between image quality, expressed as the signal-to-noise ratio (SNR) in detecting a contrasting detail, and imaging time in material testing. The model was modified to optimise the relation between the SNR in detecting a trabecular detail in cancelleous bone and the mean absorbed dose in spongiosa and skin for (rat) tibia and femur. Gastrectomized Sprague-Dawley rats were used to initiate osteoporotic changes. In order to detect differences in between gastrectomized rats and controls, spatial resolutions of 150 mm or better were needed. The minimum absorbed doses in femur spongiosa at SNR = 5 were 1mGy - 700 mGy at spatial resolutions from 100 mm to10 mm. In femur skin, the corresponding minimum absorbed doses were 2 mGy - 2000 mGy. Corresponding values for tibia were 0.3 mGy - 300 mGy for both spongiosa and skin (spatial resolution of 100 mm to10 mm). Taking 0.5 Gy as the tolerance limit for the spongiosa dose, longitudinal studies with six repeated examinations will be possible at a spatial resolution of 25 mm in femur and 17 examinations in tibia.