  Two different methods of obtaining ``effective $2\times 2$ Hamiltonians''
which include relativistic corrections to nonrelativistic calculations are
discussed, the standard Foldy--Wouthuysen transformation and what we call the
``direct Pauli reduction''. We wish to investigate under which circumstances
the two approaches yield the same result. Using a generic interaction with
harmonic time dependence we show that differences in the corresponding
effective S--matrices do arise beyond first--order perturbation theory. We
attribute them to the fact that the use of the direct reduction effective
Hamiltonian involves the additional approximation of neglecting contributions
from the negative--energy intermediate states, an approximation which is
unnecessary in the Foldy--Wouthuysen case as there the $4\times 4$ Hamiltonian
does not connect positive-- and negative--energy states. We conclude that at
least in the cases where the relativistic Hamiltonian is known, using the
direct Pauli reduction effective Hamiltonian introduces spurious relativistic
effects and therefore the Foldy--Wouthuysen reduction should be preferred.
