  We compute g_{D* D pi} and g_{B* B pi} using a framework in which all
elements are constrained by Dyson-Schwinger equation studies of QCD, and
therefore incorporates a consistent, direct and simultaneous description of
light- and heavy-quarks and the states they may constitute. We link these
couplings with the heavy-light-meson leptonic decay constants, and thereby
obtain g_{D* D pi}=15.9+2.1/-1.0 and g_{B* B pi}=30.0+3.2/-1.4. From the latter
we infer \hat-g_B=0.37+0.04/-0.02. A comparison between g_{D* D pi} and g_{B* B
pi} indicates that when the c-quark is a system's heaviest constituent,
Lambda_{QCD}/m_c-corrections are not under good control.
