Embeddings of 2-complexes into 3-manifolds

Let f : K-2 -> M-3 be an embedding of a compact, connected 2-complex into a compact, connected, orientable 3-manifold. We are interested to know, to which extent K-2 determines (up to homeomorphism) its regular neighborhood N(f(K-2)) subset of M-3. We exhibit a list of four obstructions to uniqueness, and prove that in the absence of these, the regular neighborhoods are uniquely determined: Let f, K-2, M-3 be as above and assume M-3 is prime and not a Poincare-counterexample. If N(f(K-2)) does not contain essential annuli and has connected boundary, then N is determined by K-2.