New high-resolution differential scattering cross sections are reported for the HeNe interaction. These experimental results are combined with Hartree-Fock calculations in constructing a highly accurate interatomic potential. The new potential is capable of reproducing all available experimental data judged to be sufficiently reliable. This includes properties that are highly sensitive to the very weak attractive well and its outer bowl, in addition to the weakly repulsive wall. The potential is compared to those previously proposed for HeNe, particularly to one obtained by direct inversion of differential cross section data of similarly high quality. The potential crosses through zero at σ = 2.699 Å; its minimum occurs at rm = 3.029 Å with a depth of ε = 1.83 meV.