In an orientable Haken
3
3
-manifold, given two orientable incompressible surfaces
F
F
and
S
S
transverse to each other with intersections suitably simplified, certain cut-and-paste operations along curves of intersection yield embedded incompressible surfaces. We show in this paper that, no matter how
F
F
and
S
S
are isotoped, as long as intersections are suitably simplified, exactly the same finite (possibly empty) set of isotopy classes of incompressible surfaces result from cut-and-paste operations.