  A problem with the standard Skyrme model is that Skyrmion binding energies
are around $15\%$, being much larger than the order $1\%$ binding energies of
the nuclei that they aim to describe. Here we consider theories that extend the
standard Skyrme model of pions by including rho mesons, via dimensional
deconstruction of Yang-Mills theory with an extra dimension. We report the
first results of parallel numerical computations of multi-Skyrmions in theories
of this type, including a model that reduces Skyrmion energies below those of
the standard Skyrme model whilst retaining exactly the same Faddeev-Bogomolny
energy bound. We compute all Skyrmions with baryons numbers up to 12 and find
that the inclusion of rho mesons reduces binding energies to less than $4\%,$
and therefore moves Skyrmion theory closer to experimental data. Furthermore,
we find that this dramatic reduction in binding energies is obtained without
changing the qualitative features of the Skyrmions, such as their symmetries.
