  Recent calculations of heavy quark cross sections near threshold at
next-to-next-to-leading order have found second-order corrections as large as
first-order ones. We analyse long-distance contributions to the heavy quark
potential in momentum and coordinate space and demonstrate that long-distance
contributions in momentum space are suppressed as $\Lambda_{QCD}^2/q^2$. We
then show that the long-distance sensitivity of order $\Lambda_{QCD} r$
introduced by the Fourier transform to coordinate space cancels to all orders
in perturbation theory with long-distance contributions to the heavy quark pole
mass. This leads us to define a subtraction scheme -- the `potential
subtraction scheme' -- in which large corrections to the heavy quark potential
and the `potential-subtracted' quark mass are absent. We compute the two-loop
relation of the potential-subtracted quark mass to the $\bar{\rm MS}$ quark
mass. We anticipate that threshold calculations expressed in terms of the
scheme introduced here exhibit improved convergence properties.
