  In T.Zhang, L.Xiao and R.Koniuk, Can. J. Phys. {\bf 70}, 670 (1992), a new
method was developed to calculate energy levels in QED nonrelativistic bound
states, up to order m \alpha^5. Whether or not this method could be used beyond
this order was left as an open question. In this paper, we answer this question
with the help of a nonrelativistic effective field theory, NRQED. We find that,
aside from infrared terms which had to be discarded without justification in
Zhang et al, the order m \alpha^4 and m \alpha^5 calculations give the same
results in both methods. It is shown, however, that this is due to the special
physical origin of these contributions and that the method of Zhang et al would
not give the right answer at order m \alpha^6 or higher. The separation of
scale provided by NRQED is essential to the derivation of this result.
