  The dynamics of heavy quarkonium systems in the strong coupling regime
reduces to a quantum mechanical problem with a number of potentials which may
be organized in powers of 1/m, m being the heavy quark mass. The potentials
must be calculated non-perturbatively, for instance in lattice QCD. It is well
known that the long distance behavior of the static (1/m^0) potential is well
reproduced by an effective string theory. We show that this effective string
theory, if correct, should also reproduce the long distance behavior of all 1/m
suppressed potentials. We demonstrate the practical usefulness of this result
by finding a suitable parameterization of the recently calculated 1/m
potential. We also calculate the 1/m^2 velocity dependent and spin dependent
potentials. Once Poincar\'e invariance is implemented, the shapes of most of
the spin independent potentials are fully predicted in terms of the string
tension, and the shapes of the spin dependent ones in terms of a single
parameter.
