The statistical method for calculating neutron cross sections in the unresolved resonance region has been extended to permit the construction of ladders for higher angular momentum neutrons and for all accessible spin states (and substates) of the compound nucleus. The new method is an improvement over existing methods in that a fitting procedure is adopted to ensure that the constructed sequence of resonances reproduces resonance integrals inferred from low-resolution experimental results. The s- and p-wave components of the capture cross section of 238U have been computed between 4 and 80 keV using a sequence of resonances obtained by fitting over the energy range 4 to 15 keV. The calculated 238U capture cross section is in excellent agreement with published data in the energy range 25 to 60 keV.