The well-known approximations used for finding multigroup cross sections and the Doppler coefficient are examined to determine their validity. The method involves comparing the approximate methods of one fast-reactor cross-section code (MC2) with a more rigorous treatment which removes most of the approximations. The unresolved resonance region makes a considerable contribution to the Doppler coefficient in fast reactors, and this region is treated more precisely by generating pseudo resonances using random sampling techniques within the Breit-Wigner single level formalism. A procedure is developed which ensures that the generated pseudo resonances are consistent with measured pointwise data. The resonance data is used in an ultra-fine energy group integral transporttheory code which treats the space-dependent slowing down problem in a very precise manner. A numerical comparison between the approximate methods used in MC2 and those used in the more rigorous calculations is made for a mixed carbide, sodium-cooled fast breeder reactor. Aside from some very significant detailed differences, it is shown that the approximations used in MC2 are not too severe, and that the code is adequate for determining the multigroup cross sections and the Doppler coefficient. The more rigorous method is a very time consuming and detailed procedure not well suited for design calculations. It is intended to serve as a standard, to which more approximate methods can be compared.