  The problem of bound states in effective field theories is studied. A
rescaled version of nonrelativistic effective field theory is formulated which
makes the velocity power counting of operators manifest. Results obtained using
the rescaled theory are compared with known results from NRQCD. The same ideas
are then applied to study Yukawa bound states in 1+1 and 3+1 dimensions, and to
analyze when the Yukawa potential can be replaced by a delta-function
potential. The implications of these results for the study of nucleon-nucleon
scattering in chiral perturbation theory is discussed.
