  Following the original idea of Debye, we define and extract a gauge-invariant
screening mass from the complex static in-medium heavy-quark potential
$V_{Q\bar{Q}}$, recently obtained from lattice QCD. To this end we derive a
field theoretically motivated analytic formula that faithfully reproduces both
the screened real- as well as the imaginary part of the lattice potential with
a single temperature dependent fit parameter $m_D(T)$. Using values of the real
part of $V_{Q\bar{Q}}$ in a gluonic medium, we obtain Debye masses compatible
with predictions from HTL perturbation theory.
