  We investigate the category of U(h)-free g-modules. Using a functor from this
category to the category of coherent families, we show that U(h)-free modules
only can exist when g is of type A or C. We then proceed to classify
isomorphism classes of U(h)-free modules of rank 1 in type C, which includes an
explicit construction of new simple sp(2n)-modules. Finally, we show how
translation functors can be used to obtain simple U(h)-free modules of higher
rank.
