  We derive two model-independent sum rules relating the transition matrix
elements for radiative and strong decays of excited heavy mesons to properties
of the lowest-lying heavy mesons. The sum rule for the radiative decays is an
analog of the Cabibbo-Radicati sum rule and expresses the sum of the radiative
widths in terms of the isovector charge radius of the ground state heavy meson.
Using model-dependent estimates and heavy hadron chiral perturbation theory
calculations, we show that this sum rule is close to saturation with states of
excitation energies less than 1 GeV. An analog of the Adler-Weisberger sum rule
gives an useful sum rule for the pionic widths of heavy excited mesons, which
is used to set a model-independent upper bound on the coupling of the P-wave
heavy mesons.
