Neutron elastic scattering analysing powers have been measured at 3 MeV incident energy for ^natW, ^natHg, ^natTl, ^natPb, ²⁰⁹Bi and ²³⁸U. Differential cross sections have also been measured for ^natHg, ^natTl, ^natPb and ²⁰⁸Bi. A local, phenomenological, spherical optical model analysis of these data is performed with comparison made between pure Woods-Saxon real form factors and those having surface-peaked components. The latter have been predicted in dispersion integral calculations. The effects of introducing an imaginary spin-orbit potential component are also tested. For ^natW and ²³⁸U a deformed phenomenological optical potential is used in coupled-channels calculations. Coupled-channels effects are also investigated for ²⁰⁸Pb, assuming it to be a harmonic vibrator. Microscopic calculations of real and imaginary potentials are made using the methods of Brieva and Rook, (1977,8), and Jeukenne et al. (1977). Calculation of the spin-orbit interaction is less sophisticated with an energy- and density-independent form used. At 3 MeV compound elastic scattering must be accounted for in all nuclei presently studied. This has been calculated using a recent formulation of the statistical model.