  We consider the Skyrme model with the addition of extra scalar potentials
that decrease the classical binding energies of the Skyrmions to about the 3%
level -- without altering the pion mass -- if we insist on keeping platonic
symmetries that are usually possessed by Skyrmions. A side effect of the
potentials under consideration is the smaller size of the 1-Skyrmion resulting
in a smaller moment of inertia and in turn a larger spin contribution to the
energy upon semi-classical quantization. After taking into account the quantum
contributions we find total binding energies at the 6% level.
