  We present the method and compute the strong couplings of the lowest and
first orbitally excited heavy-light mesons to a soft pion in the static heavy
quark limit on the lattice. Besides the usual g^ and \~g couplings, we were
able to make the first computation of the coupling h using the relevant radial
distributions. Our results are obtained from the simulations of QCD with Nf=2
light Wilson-Clover quarks, combined with the improved static quark actions.
The hierarchy among couplings that emerges from our study is \~g < g^ < h.
