A detailed study of the radiation following thermal neutron capture by 133Cs is reported. The statistical precision attained and the signal processing used to enhance resolution to the equivalent of 1.5 keV are combined to provide insight into the complex level structure of 134Cs. A statistical model is used to establish that the observed transitions consist mainly of primary transitions, and hence directly reflect the presence of bound levels. Comparisons are made with high resolution crystal spectrometer results to demonstrate the reliability and effectiveness of the data processing techniques employed. A neutron separation energy of 6891.584(17) keV was obtained through use of the 15N neutron binding energy and 40 low-lying levels reported from the crystal measurements. The properties of this nucleus, within the context of a statistical model, are examined and the energy dependences of level density and radiative widths are explored. Parameters such as nuclear temperature and reduced radiation widths are also given.