  A major problem in the Skyrme model is that the binding energy of skyrmions,
which model nuclei, is too high by an order of magnitude. We show that the most
popular solution to this problem, to construct models with zero classical
binding energy, still produces large binding energies when spin energy is
included. We argue that it is thus necessary to include quantum effects. We
calculate the binding energy of skyrmions including the most simple quantum
correction, that of vibrational modes in a harmonic approximation. We show that
this can give physically reasonable results for nucleon numbers N=1-8 thanks to
a remarkable cancellation between the strongly binding classical energy and the
strongly unbinding zero-point energy from vibrational modes.
