  The Contractor Renormalization (CORE) method is applied in combination with
modern effective-theory techniques to the nuclear many-body problem. A
one-dimensional--yet ``realistic''--nucleon-nucleon potential is introduced to
test these novel ideas. It is found that the magnitude of ``model-space''
(CORE) corrections diminishes considerably when an effective potential that
eliminates the hard-momentum components of the potential is first introduced.
As a result, accurate predictions for the ground-state energy of the there-body
system are made with relatively little computational effort when both
techniques are used in a complementary fashion.
