Heavy-light mesons can be studied using the 1/M expansion of NRQCD, provide
d the heavy quark mass is sufficiently large. Calculations of the S-wave ch
armed meson masses from a classically and tadpole-improved action are prese
nted. A comparison of O(1/M), O(1/M-2) and O(1/M-3) results allows converge
nce of the expansion to be discussed. It is shown that the form of discreti
zed heavy quark propagation must be chosen carefully.