  This paper studies the problems of embedding and isomorphism for countably
generated Hilbert C*-modules over commutative C*-algebras. When the fibre
dimensions differ sufficiently, relative to the dimension of the spectrum, we
show that there is an embedding between the modules. This result continues to
hold over recursive subhomogeneous C*-algebras. For certain modules, including
all modules over $C_0(X)$ when $dim X \leq 3$, isomorphism and embedding are
determined by the restrictions to the sets where the fibre dimensions are
constant. These considerations yield results for the Cuntz semigroup, including
a computation of the Cuntz semigroup for $C_0(X)$ when $dim X \leq 3$, in terms
of cohomological data about $X$.

Operator Algebras