  We analyze the heavy quark bound state spectrum using an order-dependent
conformal mapping to re-sum the perturbative expansion for current correlators.
The procedure consists of two main steps. Firstly, the Borel plane structure of
the truncated perturbative expression is modified to ensure consistency with
the operator product expansion. This is analogous to a resummation of infrared
renormalon chains. Secondly, this perturbative expansion is conformally mapped
to a new series with improved convergence properties. This approach may be
shown to induce power corrections consistent with existing condensates, and the
resulting expansion may be ordered in powers of an infrared-analytic effective
coupling. The technique is then applied to $c\bar{c}$ and $b\bar{b}$ sum rules
without any explicit introduction of vacuum condensate parameters. Ground state
masses for the vector, axial--vector, and $A'$ channels are well reproduced,
while results for the scalar--pseudoscalar mass splitting are less impressive.
