Measurements of polarized neutron-polarized 3 He scattering are reported. The target consisted of cryogenically-polarized solid 3 He, thickness 0.04 atom/b and polarization ∼ 0.4. Polarized neutrons were produced via the 3 H( p, n) 3 He or 2 H( d, n) 3 He polarization-transfer reactions. The longitudinal and transverse total cross-section differences ∆σ L and ∆σ T were measured for incident neutron energies 2-8 MeV. The results are compared to phase-shift predictions based on four different analyses of n-3 He scattering. The best agreement is obtained with a recent R-matrix analysis of A = 4 scattering and reaction data, lending strong support to the 4 He level scheme obtained in that analysis. Discrepancies with other phase-shift parameterizations of n-3 He scattering exist, attributable in most instances to one or two particular partial waves.