A precision n-α scattering experiment has been carried out in the energy interval 2-3 Mev. The angular distribution of neutrons elastically scattered by alpha particles has been measured at angles smaller than those considered in similar experiments. The phase-shift analysis of the data has led to the following results: (a) No D waves are detectable. (b) The phase shifts for the interaction in the L=0 and L=1, J=32 state agree very well with the values quoted in the literature. (c) The phase shift arising from the interaction in the L=1, J=12 state turns out to be much smaller than expected; it has been found δ121=4° at 2.37 Mev and δ121=8° at 2.87 Mev, instead of ~20° in this energy interval. It is emphasized that such an unusual experimental result should be carefully considered in theoretical investigations concerning the spin-orbit potential, and in experimental researches using helium as a polarization analyzer.