Yes, there are conditions; basically you want to maintain the hypothesis of not having incompressible tori and annuli at each stage. A really good reference for this is Morgan's essay, "On Thurston's uniformization theorem for three-dimensional manifolds", in Morgan, John W.; Bass, Hyman, The Smith conjecture (New York, 1979), Pure Appl. Math. 112, Boston, MA: Academic Press, pp. 37–125.  I'd suggest looking there.