  We present the complete solution to the so-called ``Yukawa problem'' of the
Skyrme model. This refers to the perceived difficulty of reproducing---purely
from soliton physics---the usual pseudovector pion-nucleon coupling, echoed by
pion coupling to the higher spin/isospin baryons $(I=J=3/2 , 5/2 , \cdots ,
N_c/2 )$ in a manner fixed by large-$N_c$ group theory. The solution involves
surprisingly elegant interplay between the classical and quantum properties of
a new configuration, the ``new improved skyrmion''. This is the near-hedgehog
obtained by minimizing the usual skyrmion mass functional augmented by an
all-important isorotational kinetic term. The numerics are pleasing: a $\Delta$
decay width within a few MeV of its measured value, and furthermore, the
higher-spin baryons $(I=J \ge 5/2 )$ with widths so large ($\Gamma > 800 MeV$)
that these undesirable large-$N_c$ artifacts effectively drop out of the
spectrum, and pose no phenomenological problem. Beyond these specific results,
we ground the Skyrme model in the Feynman Path Integral, and set up a
transparent collective coordinate formalism that makes maximal use of the
$1/N_c$ expansion. This approach elucidates the connection between skyrmions on
the one hand, and Feynman diagrams in an effective field theory on the other.
