  We study under what conditions massive fields can be "frozen" rather than
integrated out in certain four dimensional theories with global or local N=1
supersymmetry. We focus on models without gauge fields, admitting a
superpotential of the form W = W0(H) + epsilon W1(H,L), with epsilon << 1,
where H and L schematically denote the heavy and light chiral superfields. We
find that the fields H can always be frozen to constant values H0, if they
approximately correspond to supersymmetric solutions along the H directions,
independently of the form of the Kahler potential K for H and L, provided K is
sufficiently regular. In supergravity W0 is required to be of order epsilon at
the vacuum to ensure a mass hierarchy between H and L. The backreaction induced
by the breaking of supersymmetry on the heavy fields is always negligible,
leading to suppressed F^H--terms. For factorizable Kahler potentials W0 can
instead be generic. Our results imply that the common way complex structure and
dilaton moduli are stabilized, as in Phys. Rev. D 68 (2003) 046005 by Kachru et
al., for instance, is reliable to a very good accuracy, provided W0 is small
enough.
