Thermal-neutron diffusion lengths have been measured with an accuracy of typically ½% in aqueous absorbing solution contained in a tank adjacent to a reactor thermal column. Both pure water and boric acid solutions were used at 22.3 and 65°C, and solutions of cadmium and gadolinium salts at the lower temperature. Ten concentrations of each absorber were used. Two of the measured diffusion lengths for cadmium yield space eigenvalues which violate the (ΣT)min limit of Corngold. Slight diffusion cooling occurs in cadmium solutions in contrast to marked heating effects in boron and gadolinium solutions. Theoretical predictions of diffusion lengths have been obtained by a B2 solution of the transport equation. Four scattering models were used: the Nelkin model, Haywood model, and two further models consisting of modifications to each of these. The modifications highlight particular parts of the hydrogen-atom generalized frequency distribution. A Laguerre polynomial expansion technique is investigated but found to be unsuitable for the analysis of non-1/v poison data.