  The J$^{\pi}$=0$^+$ ground state of a drop of 8 neutrons and the lowest
1/2$^-$ and 3/2$^-$ states of 7-neutron drops, all in an external well, are
computed accurately with variational and Green's function Monte Carlo methods
for a Hamiltonian containing the Argonne $v_{18}$ two-nucleon and Urbana IX
three-nucleon potentials. These states are also calculated using Skyrme-type
energy-density functionals. Commonly used functionals overestimate the central
density of these drops and the spin-orbit splitting of 7-neutron drops.
Improvements in the functionals are suggested.
