  We consider the dielectric Skyrme model proposed recently, with and without
the addition of the standard pion mass term. Then we write down
Bogomol'nyi-type energy bounds for both the massless and massive cases. We
further show that, except for when taking the strict BPS limit, the Skyrmions
are made of 3 orthogonal dipoles that can always be placed in their attractive
channel and form bound states. Finally, we study the model numerically and
discover that, long before realistic binding energies are reached, the
Skyrmions become bound states of well-separated point-particle-like Skyrmions.
By going sufficiently close to the BPS limit, we are able to obtain classical
binding energies of realistic values compared with experiments.
