Dipole radiation in QCD is derived to the second order in
$\alpha_s$. A power-like evolution of the spin-singlet heavy quark
operators is obtained to the same accuracy. We give an ${\cal
O}(\alpha_s^2)$ relation between the short-distance low-scale running
heavy quark mass and the $\overline{\rm MS}$ mass. We discuss the
properties of an effective QCD coupling $\alpha_s^{(d)}(E)$ which
governs the dipole radiation. We argue that this coupling is
advantageous for describing heavy quark physics.