  The true muonium $(\mu\bar{\mu})$ bound state presents an interesting test of
light-cone quantization techniques. In addition to exhibiting the standard
problems of handling non-perturbative calculations, true muonium requires
correct treatment of $e\bar{e}$ Fock-state contributions. Having previously
produced a crude model of true muonium using the method of iterated resolvents,
our current work has focused on the inclusion of the box diagrams to improve
the cutoff-dependent issues of the model. Further, a parallel computer code,
TMSWIFT, allowing for smaller numerical uncertainties, has been developed. This
work focuses on the current state of these efforts to develop a model of true
muonium that is testable at near-term experiments.
