  A complete classification is presented of elliptic and K3 fibrations
birational to certain mildly singular complex Fano 3-folds. Detailed proofs are
given for one example case, namely that of a general hypersurface X of degree
30 in weighted P^4 with weights 1,4,5,6,15; but our methods apply more
generally. For constructing birational maps from X to elliptic and K3
fibrations we use Kawamata blowups and Mori theory to compute anticanonical
rings; to exclude other possible fibrations we make a close examination of the
strictly canonical singularities of (X,(1/n)H), where H is the linear system
associated to the putative birational map and n is its anticanonical degree.
